Question 1

The graph of a quadratic function is given. Determine the function's equation.
-
A) $f ( x ) = ( x + 1 ) ^ { 2 } + 1$
B) $g ( x ) = ( x + 1 ) ^ { 2 } - 1$
C) $h ( x ) = ( x - 1 ) ^ { 2 } + 1$
D) $j ( x ) = ( x - 1 ) ^ { 2 } - 1$

Accepted Answer

A

Question 2

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$y + 4 = ( x - 2 ) ^ { 2 }$$
A) $( 2 , - 4 )$
B) $( - 2 , - 4 )$
C) $( 4,2 )$
D) $( 4 , - 2 )$

Accepted Answer

The vertex form of a parabola is $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex. Comparing this to the given equation $y + 4 = (x - 2)^2$, we can rewrite it as $y = (x - 2)^2 - 4$, showing the vertex is at $(2, -4)$.

Question 3

The graph of a quadratic function is given. Determine the function's equation.
-
A) $f ( x ) = x ^ { 2 } - 6 x + 9$
B) $g ( x ) = x ^ { 2 } + 6 x + 9$
C) $h ( x ) = x ^ { 2 } - 3$
D) $j ( x ) = x ^ { 2 } + 3$

Accepted Answer

The graph intersects the y-axis at 9, which means that the constant term in the quadratic function is 9. Furthermore, the vertex of the parabola is at (3,0), which corresponds to the axis of symmetry being x=3. This means that x = 3 is the value of the line of symmetry of the parabola. Since the parabola opens upwards, the coefficient of x^2 is positive. Putting all of this information together, we get the equation f(x) = (x-3)^2 + 9, which simplifies to f(x) = x^2 - 6x + 9. Therefore, the answer is A.

Question 4

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = ( x + 4 ) ^ { 2 } + 9$$
A) $( - 4,9 )$
B) $( - 9,4 )$
C) $( 9 , - 16 )$
D) $( 9 , - 4 )$

Accepted Answer

The quadratic function is already in vertex form, which is $f(x)=(x-h)^2+k$ where the vertex is at $(h,k)$. Therefore, the vertex is at $(-4,9)$.

Question 5

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = 8 - ( x + 5 ) ^ { 2 }$$
A) $( - 5,8 )$
B) $( 5,8 )$
C) $( 8,5 )$
D) $( 8 , - 5 )$

Accepted Answer

The quadratic function is in vertex form, which is $f(x)=a-(x-h)^2$. The vertex of the parabola is at the point $(h,a)$. Therefore, the vertex of $f(x)=8-(x+5)^2$ is $(-5,8)$.

Question 6

The graph of a quadratic function is given. Determine the function's equation.
-

A) $h ( x ) = ( x - 2 ) ^ { 2 } + 2$
B) $g ( x ) = ( x + 2 ) ^ { 2 } - 2$
C) $f ( x ) = ( x + 2 ) ^ { 2 } + 2$
D) $j ( x ) = ( x - 2 ) ^ { 2 } - 2$

Accepted Answer

The answer of The graph of a quadratic function is...

Question 7

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = x ^ { 2 } + 2 x - 6$$
A) $( - 1 , - 7 )$
B) $( 1 , - 3 )$
C) $( 2,2 )$
D) $( - 1 , - 9 )$

Accepted Answer

The vertex of a parabola defined by $f(x) = ax^2 + bx + c$ can be found using the formula $(- \frac{b}{2a}, f(- \frac{b}{2a}))$. For $f(x) = x^2 + 2x - 6$, $a = 1$, $b = 2$, so the x-coordinate of the vertex is $- \frac{2}{2(1)} = -1$. Plugging this back into the function gives $f(-1) = (-1)^2 + 2(-1) - 6 = 1 - 2 - 6 = -7$. Therefore, the vertex is $(-1, -7)$.

Question 8

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = ( x + 7 ) ^ { 2 } - 4$$
A) $( - 7 , - 4 )$
B) $( 7,4 )$
C) $( 7 , - 4 )$
D) $( - 7,4 )$

Accepted Answer

The vertex form of a parabola is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. The given equation is already in vertex form with $h = -7$ and $k = -4$, making the vertex $(-7, -4)$.

Question 9

The graph of a quadratic function is given. Determine the function's equation.
-
A) $j ( x ) = - x ^ { 2 } + 2$
B) $g ( x ) = - x ^ { 2 } + 4 x + 4$
C) $h ( x ) = - x ^ { 2 } - 2$
D) $f ( x ) = - x ^ { 2 } - 4 x - 4$

Accepted Answer

The answer of The graph of a quadratic function is...

Question 10

The graph of a quadratic function is given. Determine the function's equation.
-
A) $j ( x ) = x ^ { 2 } + 3$
B) $g ( x ) = x ^ { 2 } + 6 x + 9$
C) $h ( x ) = x ^ { 2 } - 3$
D) $f ( x ) = x ^ { 2 } - 6 x + 9$

Accepted Answer

The answer of The graph of a quadratic function is...

Question 11

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = ( x - 5 ) ^ { 2 } - 5$$
A) $( 5 , - 5 )$
B) $( 5,5 )$
C) $( 0 , - 5 )$
D) $( - 5,0 )$

Accepted Answer

The vertex form of a parabola is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. For $f(x) = (x - 5)^2 - 5$, the vertex is $(5, -5)$.

Question 12

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = x ^ { 2 } - 4$$
A) $( 0 , - 4 )$
B) $( 1,0 )$
C) $( 0,4 )$
D) $( 4,0 )$

Accepted Answer

The vertex form of a parabola is $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex. For the given function $f(x) = x^2 - 4$, it is already in a form close to the vertex form with $a = 1$, $h = 0$, and $k = -4$. Therefore, the vertex is at $(0, -4)$.

Question 13

The graph of a quadratic function is given. Determine the function's equation.
-
A) $j ( x ) = ( x - 3 ) ^ { 2 } - 3$
B) $g ( x ) = ( x + 3 ) ^ { 2 } - 3$
C) $h ( x ) = ( x - 3 ) ^ { 2 } + 3$
D) $f ( x ) = ( x + 3 ) ^ { 2 } + 3$

Accepted Answer

The answer of The graph of a quadratic function is...

Question 14

The graph of a quadratic function is given. Determine the function's equation.
-
A) $h ( x ) = x ^ { 2 } - 2$
B) $g ( x ) = x ^ { 2 } + 4 x + 4$
C) $f ( x ) = x ^ { 2 } - 4 x + 4$
D) $j ( x ) = x ^ { 2 } + 2$

Accepted Answer

The answer of The graph of a quadratic function is...

Question 15

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = 11 ( x - 5 ) ^ { 2 } + 9$$
A) $( 5,9 )$
B) $( 11,5 )$
C) $( - 5,9 )$
D) $( 9 , - 5 )$

Accepted Answer

The vertex of a parabola in the form $f(x) = a(x-h)^2 + k$ is at $(h,k)$. Therefore, in this case, the vertex is at $(5,9)$.

Question 16

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 8$$
A) $( 2 , - 8 )$
B) $( - 8,2 )$
C) $( - 2 , - 8 )$
D) $( - 7 , - 2 )$

Accepted Answer

The given quadratic function is in vertex form, where the vertex is at the point (h,k) given by the equation f(x) = a(x-h)^2 + k. Therefore, we can read off the vertex as (2,-8) where h=2 and k=-8. Thus, the answer is choice A.

Question 17

The graph of a quadratic function is given. Determine the function's equation.
-
A) $h ( x ) = - x ^ { 2 } - 1$
B) $g ( x ) = - x ^ { 2 } + 2 x + 1$
C) $\mathrm { j } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 1$
D) $f ( x ) = - x ^ { 2 } - 2 x - 1$

Accepted Answer

The answer of The graph of a quadratic function is...

Question 18

The graph of a quadratic function is given. Determine the function's equation.
-
A) $g ( x ) = ( x + 3 ) ^ { 2 } - 3$
B) $f ( x ) = ( x + 3 ) ^ { 2 } + 3$
C) $h ( x ) = ( x - 3 ) ^ { 2 } + 3$
D) $j ( x ) = ( x - 3 ) ^ { 2 } - 3$

Accepted Answer

The answer of The graph of a quadratic function is...

Question 19

The graph of a quadratic function is given. Determine the function's equation.
-
A) $g ( x ) = x ^ { 2 } + 2 x + 1$
B) $f ( x ) = x ^ { 2 } - 2 x + 1$
C) $h ( x ) = x ^ { 2 } - 1$
D) $j ( x ) = x ^ { 2 } + 1$

Accepted Answer

The answer of The graph of a quadratic function is...

Question 20

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = x ^ { 2 } + 5$$
A) $( 0,5 )$
B) $( - 5,0 )$
C) $( 0 , - 5 )$
D) $( 5,0 )$

Accepted Answer

The given quadratic function is in the standard form, $f(x) = ax^2 + bx + c$, where $a=1$, $b=0$, and $c=5$. The $x$-coordinate of the vertex of this parabola is at $x=-\frac{b}{2a}=0$. To find the $y$-coordinate of the vertex, we plug in $x=0$ into the function: $f(0) = 0^2 + 5 = 5$. Therefore, the coordinates of the vertex are $(0,5)$, which is choice A.

Quiz 3: Polynomial and Rational Functions

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $y + 4 = ( x - 2 ) ^ { 2 }$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) f ( x ) = x ^ { 2 } - 6 x + 9 B) g ( x ) = x ^ { 2 } + 6 x + 9 C) h ( x ) = x ^ { 2 } - 3 D) j ( x ) = x ^ { 2 } + 3$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x + 4 ) ^ { 2 } + 9$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 8 - ( x + 5 ) ^ { 2 }$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } + 2 x - 6$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x + 7 ) ^ { 2 } - 4$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) j ( x ) = - x ^ { 2 } + 2 B) g ( x ) = - x ^ { 2 } + 4 x + 4 C) h ( x ) = - x ^ { 2 } - 2 D) f ( x ) = - x ^ { 2 } - 4 x - 4$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) j ( x ) = x ^ { 2 } + 3 B) g ( x ) = x ^ { 2 } + 6 x + 9 C) h ( x ) = x ^ { 2 } - 3 D) f ( x ) = x ^ { 2 } - 6 x + 9$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x - 5 ) ^ { 2 } - 5$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } - 4$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) h ( x ) = x ^ { 2 } - 2 B) g ( x ) = x ^ { 2 } + 4 x + 4 C) f ( x ) = x ^ { 2 } - 4 x + 4 D) j ( x ) = x ^ { 2 } + 2$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 11 ( x - 5 ) ^ { 2 } + 9$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 8$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) g ( x ) = x ^ { 2 } + 2 x + 1 B) f ( x ) = x ^ { 2 } - 2 x + 1 C) h ( x ) = x ^ { 2 } - 1 D) j ( x ) = x ^ { 2 } + 1$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } + 5$

Quiz 3: Polynomial and Rational Functions

The graph of a quadratic function is given. Determine the function's equation. -

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - y+4=(x−2) 2y + 4 = ( x - 2 ) ^ { 2 }y+4=(x−2) 2

The graph of a quadratic function is given. Determine the function's equation. -

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x) =(x+4) 2+9f ( x ) = ( x + 4 ) ^ { 2 } + 9f(x) =(x+4) 2+9

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x) =8−(x+5) 2f ( x ) = 8 - ( x + 5 ) ^ { 2 }f(x) =8−(x+5) 2

The graph of a quadratic function is given. Determine the function's equation. -

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x) =x2+2x−6f ( x ) = x ^ { 2 } + 2 x - 6f(x) =x2+2x−6

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x) =(x+7) 2−4f ( x ) = ( x + 7 ) ^ { 2 } - 4f(x) =(x+7) 2−4

The graph of a quadratic function is given. Determine the function's equation. -

The graph of a quadratic function is given. Determine the function's equation. -

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x) =(x−5) 2−5f ( x ) = ( x - 5 ) ^ { 2 } - 5f(x) =(x−5) 2−5

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x) =x2−4f ( x ) = x ^ { 2 } - 4f(x) =x2−4

The graph of a quadratic function is given. Determine the function's equation. -

The graph of a quadratic function is given. Determine the function's equation. -

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x) =11(x−5) 2+9f ( x ) = 11 ( x - 5 ) ^ { 2 } + 9f(x) =11(x−5) 2+9

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x) =−7(x−2) 2−8f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 8f(x) =−7(x−2) 2−8

The graph of a quadratic function is given. Determine the function's equation. -

The graph of a quadratic function is given. Determine the function's equation. -

The graph of a quadratic function is given. Determine the function's equation. -

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x) =x2+5f ( x ) = x ^ { 2 } + 5f(x) =x2+5

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $y + 4 = ( x - 2 ) ^ { 2 }$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) f ( x ) = x ^ { 2 } - 6 x + 9 B) g ( x ) = x ^ { 2 } + 6 x + 9 C) h ( x ) = x ^ { 2 } - 3 D) j ( x ) = x ^ { 2 } + 3$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x + 4 ) ^ { 2 } + 9$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 8 - ( x + 5 ) ^ { 2 }$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } + 2 x - 6$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x + 7 ) ^ { 2 } - 4$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) j ( x ) = - x ^ { 2 } + 2 B) g ( x ) = - x ^ { 2 } + 4 x + 4 C) h ( x ) = - x ^ { 2 } - 2 D) f ( x ) = - x ^ { 2 } - 4 x - 4$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) j ( x ) = x ^ { 2 } + 3 B) g ( x ) = x ^ { 2 } + 6 x + 9 C) h ( x ) = x ^ { 2 } - 3 D) f ( x ) = x ^ { 2 } - 6 x + 9$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x - 5 ) ^ { 2 } - 5$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } - 4$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) h ( x ) = x ^ { 2 } - 2 B) g ( x ) = x ^ { 2 } + 4 x + 4 C) f ( x ) = x ^ { 2 } - 4 x + 4 D) j ( x ) = x ^ { 2 } + 2$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 11 ( x - 5 ) ^ { 2 } + 9$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 8$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) g ( x ) = x ^ { 2 } + 2 x + 1 B) f ( x ) = x ^ { 2 } - 2 x + 1 C) h ( x ) = x ^ { 2 } - 1 D) j ( x ) = x ^ { 2 } + 1$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } + 5$