Question 1

If  , match each condition on the constants to the appropriate graph of the curve.
​
a.  b.  and  c.  and  have opposite signs
d.  and  have same signs
-an ellipse

Accepted Answer

The answer of If  , match each condition on...

Question 2

Identify the curve.
​
​  ​
This curve is __________ (parabola, line, circle, hyperbola).

Accepted Answer

The answer of Identify the curve.
​
​  ​
This curve is...

Question 3

Sketch the graph of the equation. ​  ​

Accepted Answer

The answer of Sketch the graph of the equation. ​...

Question 4

Sketch the curve. ​  ​

Accepted Answer

The answer of Sketch the curve. ​  ​
...

Question 5

If  , match each condition on the constants to the appropriate graph of the curve.
​
a.  b.  and  c.  and  have opposite signs
d.  and  have same signs
-a line

Accepted Answer

The answer of If  , match each condition on...

Question 6

A parabolic archway has the dimensions shown in the figure. Find the equation of the parabolic portion.
​
​  ft,  ft,  ft,  ft
​

Accepted Answer

The answer of A parabolic archway has the dimensions shown...

Question 7

Sketch the graph of the equation. ​  ​

Accepted Answer

The answer of Sketch the graph of the equation. ​...

Question 8

Identify the curve.
​
​  ​
This curve is __________ (line, circle, parabola, hyperbola).

Accepted Answer

The answer of Identify the curve.
​
​  ​
This curve is...

Question 9

Sketch the curve. ​
​  ​

Accepted Answer

The answer of Sketch the curve. ​
​  ​
...

Question 10

Sketch the curve. ​
​  ​

Accepted Answer

The curve appears to be a parabola opening upwards. Choice B represents a correctly drawn parabola with the vertex at the origin and the axis of symmetry along the y-axis. The other choices do not accurately represent a parabola.

Question 11

If  , match each condition on the constants to the appropriate graph of the curve.
​
a.  b.  and  c.  and  have opposite signs
d.  and  have same signs
-a circle

Accepted Answer

The answer of If  , match each condition on...

Question 12

Identify the curve. ​
​  ​

Accepted Answer

The answer of Identify the curve. ​
​  ​
...

Question 13

If  , match each condition on the constants to the appropriate graph of the curve.
​
a.  b.  and  c.  and  have opposite signs
d.  and  have same signs
-a hyperbola

Accepted Answer

The answer of If  , match each condition on...

Question 14

Identify the curve. ​  ​

Accepted Answer

The answer of Identify the curve. ​  ​
...

Question 15

Beams of light parallel to the axis of the parabolic mirror shown in the figure strike the mirror and are reflected. Find the distance from the vertex to the point where the beams concentrate. ​
A = 12 ft, b = 8 ft
​  ​

Accepted Answer

The focal length of a parabolic mirror is equal to one-fourth of the distance between the vertex and the focus, i.e. $f=\frac{A}{4}$.
In this case, $A=12$ ft, so $f=\frac{12}{4}=3$ ft.
To convert this to inches, we multiply by 12, giving $f=36$ in.
Thus, the focus is 36 inches from the vertex on the axis of the parabola.
But the question asks for the distance from the vertex to the point where the beams concentrate, which is twice the focal length. 
Therefore, the distance from the vertex to the point where the beams concentrate is $2f=2\cdot 36=\boxed{72}$ inches or 6 feet.

Question 16

Sketch the hyperbola with distance between the foci 10 units and the difference of the distances 6 units. ​

Accepted Answer

The equation of the hyperbola with distance between the foci $2c=10$ and the difference of the distances $2a=6$ is given by $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, where $c^2=a^2+b^2$. Solving for $a$ and $b$, we have $a=3$ and $b=4$. Thus, the equation of the hyperbola is $\frac{x^2}{9}-\frac{y^2}{16}=1$, which corresponds to the graph in choice (C).

Question 17

Sketch the graph of the equation. ​  ​

Accepted Answer

The answer of Sketch the graph of the equation. ​...

Question 18

Beams of light parallel to the axis of the parabolic mirror shown in the figure strike the mirror and are reflected. Find the distance from the vertex to the point where the beams concentrate.
​  ft,  ft
​  ​
The focus is __________ in. from the vertex on the axis of the parabola.

Accepted Answer

The answer of Beams of light parallel to the axis...

Question 19

A parabolic archway has the dimensions shown in the figure. Find the equation of the parabolic portion. ​  ft,  ft,  ft,  ft
​  ​

Accepted Answer

The answer of A parabolic archway has the dimensions shown...

Question 20

Sketch the graph of the equation. ​  ​

Accepted Answer

The equation is a quadratic equation in standard form with a positive coefficient for the squared term. Therefore, it will open upwards and have a minimum point. The vertex of the parabola can be found using the formula (-b/2a, f(-b/2a)). In this case, the vertex is approximately (0.364, -3.631) which confirms that the parabola opens upwards. Choice B is the only option that correctly reflects this upward opening parabola.

Quiz 15: The Nature of Graphs and Functions

If , match each condition on the constants to the appropriate graph of the curve. a. b. and c. and have opposite signs d. and have same signs -an ellipse

Identify the curve. This curve is __________ (parabola, line, circle, hyperbola).

Sketch the graph of the equation.

Sketch the curve.

If , match each condition on the constants to the appropriate graph of the curve. a. b. and c. and have opposite signs d. and have same signs -a line

A parabolic archway has the dimensions shown in the figure. Find the equation of the parabolic portion. ft, ft, ft, ft

Sketch the graph of the equation.

Identify the curve. This curve is __________ (line, circle, parabola, hyperbola).

Sketch the curve.

Sketch the curve.

If , match each condition on the constants to the appropriate graph of the curve. a. b. and c. and have opposite signs d. and have same signs -a circle

Identify the curve.

If , match each condition on the constants to the appropriate graph of the curve. a. b. and c. and have opposite signs d. and have same signs -a hyperbola

Identify the curve.

Beams of light parallel to the axis of the parabolic mirror shown in the figure strike the mirror and are reflected. Find the distance from the vertex to the point where the beams concentrate. A = 12 ft, b = 8 ft

Sketch the hyperbola with distance between the foci 10 units and the difference of the distances 6 units.

Sketch the graph of the equation.

Beams of light parallel to the axis of the parabolic mirror shown in the figure strike the mirror and are reflected. Find the distance from the vertex to the point where the beams concentrate. ft, ft The focus is __________ in. from the vertex on the axis of the parabola.

A parabolic archway has the dimensions shown in the figure. Find the equation of the parabolic portion. ft, ft, ft, ft

Sketch the graph of the equation.

Quiz 15: The Nature of Graphs and Functions

If , match each condition on the constants to the appropriate graph of the curve. ​ a. b. and c. and have opposite signs d. and have same signs -an ellipse

Identify the curve. ​ ​ ​ This curve is __________ (parabola, line, circle, hyperbola).

Sketch the graph of the equation. ​ ​

Sketch the curve. ​ ​

If , match each condition on the constants to the appropriate graph of the curve. ​ a. b. and c. and have opposite signs d. and have same signs -a line

A parabolic archway has the dimensions shown in the figure. Find the equation of the parabolic portion. ​ ​ ft, ft, ft, ft ​

Sketch the graph of the equation. ​ ​

Identify the curve. ​ ​ ​ This curve is __________ (line, circle, parabola, hyperbola).

Sketch the curve. ​ ​ ​

Sketch the curve. ​ ​ ​

If , match each condition on the constants to the appropriate graph of the curve. ​ a. b. and c. and have opposite signs d. and have same signs -a circle

Identify the curve. ​ ​ ​

If , match each condition on the constants to the appropriate graph of the curve. ​ a. b. and c. and have opposite signs d. and have same signs -a hyperbola

Identify the curve. ​ ​

Beams of light parallel to the axis of the parabolic mirror shown in the figure strike the mirror and are reflected. Find the distance from the vertex to the point where the beams concentrate. ​ A = 12 ft, b = 8 ft ​ ​

Sketch the hyperbola with distance between the foci 10 units and the difference of the distances 6 units. ​

Sketch the graph of the equation. ​ ​

Beams of light parallel to the axis of the parabolic mirror shown in the figure strike the mirror and are reflected. Find the distance from the vertex to the point where the beams concentrate. ​ ft, ft ​ ​ The focus is __________ in. from the vertex on the axis of the parabola.

A parabolic archway has the dimensions shown in the figure. Find the equation of the parabolic portion. ​ ft, ft, ft, ft ​ ​

Sketch the graph of the equation. ​ ​

If , match each condition on the constants to the appropriate graph of the curve. a. b. and c. and have opposite signs d. and have same signs -an ellipse

Identify the curve. This curve is __________ (parabola, line, circle, hyperbola).

Sketch the graph of the equation.

Sketch the curve.

If , match each condition on the constants to the appropriate graph of the curve. a. b. and c. and have opposite signs d. and have same signs -a line

A parabolic archway has the dimensions shown in the figure. Find the equation of the parabolic portion. ft, ft, ft, ft

Sketch the graph of the equation.

Identify the curve. This curve is __________ (line, circle, parabola, hyperbola).

Sketch the curve.

Sketch the curve.

If , match each condition on the constants to the appropriate graph of the curve. a. b. and c. and have opposite signs d. and have same signs -a circle

Identify the curve.

If , match each condition on the constants to the appropriate graph of the curve. a. b. and c. and have opposite signs d. and have same signs -a hyperbola

Identify the curve.

Beams of light parallel to the axis of the parabolic mirror shown in the figure strike the mirror and are reflected. Find the distance from the vertex to the point where the beams concentrate. A = 12 ft, b = 8 ft

Sketch the hyperbola with distance between the foci 10 units and the difference of the distances 6 units.

Sketch the graph of the equation.

Beams of light parallel to the axis of the parabolic mirror shown in the figure strike the mirror and are reflected. Find the distance from the vertex to the point where the beams concentrate. ft, ft The focus is __________ in. from the vertex on the axis of the parabola.

A parabolic archway has the dimensions shown in the figure. Find the equation of the parabolic portion. ft, ft, ft, ft

Sketch the graph of the equation.