Question 1

Write an equation for the parabola with vertex at the origin.&#10;

Accepted Answer

The given parabola has its vertex at the origin and is symmetric with respect to the y-axis, indicating it opens upwards or downwards. Since it passes through (2,2), only $x^2 = 2y$ satisfies this condition, as it represents a parabola opening upwards with the correct orientation and position.

Question 2

Write an equation for the parabola with vertex at the origin.&#10;

Accepted Answer

The given parabola has its vertex at the origin and opens upward, which matches the standard form $y = ax^2$. Substituting the point $(\sqrt{2}, 2)$ into $y = ax^2$ gives $2 = a(\sqrt{2})^2$, simplifying to $2 = 2a$, which means $a = 1$. Therefore, the equation is $y = x^2$.

Question 3

Write an equation for the parabola with vertex at the origin.&#10;

Accepted Answer

The equation of a parabola with vertex at the origin and focus $(0, -p)$ is $x^2 = -4py$. So, the equation of the parabola with vertex at the origin and focus $(0, -\frac{1}{11})$ is $x^2 = -4\left(-\frac{1}{11}\right)y = \frac{4}{11}y$.

Question 4

Match the equation of the parabola with the appropriate description.&#10;

Accepted Answer

The given equation is in the form $x = a(y - k)^2 + h$, which represents a parabola that opens to the right or left. By comparing it to the standard form, we can find the vertex $(h, k)$. Rearranging the given equation to match the standard form, we get $x + 2 = 2(y + 7)^2$. Here, $h = -2$ and $k = -7$, so the vertex is $(-2, -7)$.

Question 5

Match the equation of the parabola with the appropriate description.&#10; &#10;A) Opens up&#10;B) Opens down&#10;C) Opens left&#10;D) Opens right

Accepted Answer

The equation is in the form $x = ay^2 + by + c$, which indicates a parabola that opens either left or right. Since the coefficient of $y^2$ (which is 2) is positive, the parabola opens to the right.

Question 6

Write an equation for the parabola with vertex at the origin.&#10;

Accepted Answer

The parabola with a horizontal axis and vertex at the origin has the form $y^2 = 4px$. The focus is $(- \frac{1}{7}, 0)$, so $p = -\frac{1}{7}$. Thus, the equation is $y^2 = 4(-\frac{1}{7})x = -\frac{4}{7}x$.

Question 7

Write an equation for the parabola with vertex at the origin.&#10;

Accepted Answer

The parabola has a horizontal axis of symmetry because the focus is on the x-axis. The distance from the vertex to the focus is 6, so the equation is $y^2 = 4px$ where $p = 6$, giving $y^2 = 24x$.

Question 8

Write an equation for the parabola with vertex at the origin.&#10;

Accepted Answer

A parabola opening to the left with its vertex at the origin is of the form $y^2 = 4px$, where $p < 0$ because it opens to the left. Given the point $(-8, 8)$, we substitute $y = 8$ and $x = -8$ into the equation to find $p$. The correct equation that fits this description is $y^2 = -8x$, which matches choice B.

Question 9

Match the equation of the parabola with the appropriate description.&#10;

Accepted Answer

The given equation is in the form $y - k = a(x - h)^2$, where $(h, k)$ is the vertex of the parabola. Comparing, we find the vertex is at $(-15, -2)$.

Question 10

Match the equation of the parabola with the appropriate description.&#10; &#10;A) Opens left&#10;B) Opens right&#10;C) Opens down&#10;D) Opens up

Accepted Answer

The given equation is in the form $x = ay^2 + by + c$, which represents a parabola that opens either left or right. Since the coefficient of $y^2$ is negative (-3), the parabola opens to the left.

Question 11

Match the equation of the parabola with the appropriate description.&#10; &#10;A) Opens left&#10;B) Opens right&#10;C) Opens down&#10;D) Opens up

Accepted Answer

The answer of Match the equation of the parabola with...

Question 12

Write an equation for the parabola with vertex at the origin.&#10;

Accepted Answer

The answer of Write an equation for the parabola with...

Question 13

Match the equation of the parabola with the appropriate description.&#10;

Accepted Answer

The answer of Match the equation of the parabola with...

Question 14

Match the equation of the parabola with the appropriate description.&#10;

Accepted Answer

The answer of Match the equation of the parabola with...

Question 15

Write an equation for the parabola with vertex at the origin.&#10;

Accepted Answer

The answer of Write an equation for the parabola with...

Question 16

Match the equation of the parabola with the appropriate description.&#10; &#10;A) Opens left&#10;B) Opens up&#10;C) Opens down&#10;D) Opens right

Accepted Answer

The answer of Match the equation of the parabola with...

Question 17

Match the equation of the parabola with the appropriate description.&#10;

Accepted Answer

The answer of Match the equation of the parabola with...

Question 18

Write an equation for the parabola with vertex at the origin.&#10;

Accepted Answer

The answer of Write an equation for the parabola with...

Question 19

Write an equation for the parabola with vertex at the origin.&#10;

Accepted Answer

The answer of Write an equation for the parabola with...

Question 20

Match the equation of the parabola with the appropriate description.&#10; &#10;A) Opens left&#10;B) Opens down&#10;C) Opens right&#10;D) Opens up

Accepted Answer

The answer of Match the equation of the parabola with...

Question 21

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator.&#10;

Accepted Answer

The answer of Determine the two equations necessary to graph...

Question 22

Write an equation for the parabola.&#10;

Accepted Answer

The answer of Write an equation for the parabola.&#10; ...

Question 23

Graph the parabola.&#10;

Accepted Answer

The answer of Graph the parabola.&#10;   ...

Question 24

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator.&#10;

Accepted Answer

The answer of Determine the two equations necessary to graph...

Question 25

Write an equation for the parabola.&#10;

Accepted Answer

The answer of Write an equation for the parabola.&#10; ...

Question 26

Graph the parabola.&#10;

Accepted Answer

The answer of Graph the parabola.&#10; ...

Question 27

Write an equation for the parabola.&#10;

Accepted Answer

The answer of Write an equation for the parabola.&#10; ...

Question 28

Graph the parabola.&#10;

Accepted Answer

The answer of Graph the parabola.&#10;   ...

Question 29

Write an equation for the parabola.&#10;

Accepted Answer

The answer of Write an equation for the parabola.&#10; ...

Question 30

Write an equation for the parabola.&#10;

Accepted Answer

The answer of Write an equation for the parabola.&#10; ...

Question 31

Graph the parabola.&#10;  8

Accepted Answer

The answer of Graph the parabola.&#10;  8  ...

Question 32

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator.&#10;

Accepted Answer

The answer of Determine the two equations necessary to graph...

Question 33

Write an equation for the parabola.&#10;

Accepted Answer

The answer of Write an equation for the parabola.&#10; ...

Question 34

Write an equation for the parabola.&#10;

Accepted Answer

The answer of Write an equation for the parabola.&#10; ...

Question 35

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator.&#10;

Accepted Answer

The answer of Determine the two equations necessary to graph...

Question 36

Graph the parabola.&#10;

Accepted Answer

The answer of Graph the parabola.&#10;   ...

Question 37

Write an equation for the parabola.&#10;

Accepted Answer

The answer of Write an equation for the parabola.&#10; ...

Question 38

Write an equation for the parabola.&#10;

Accepted Answer

The answer of Write an equation for the parabola.&#10; ...

Question 39

Graph the parabola.&#10;

Accepted Answer

The answer of Graph the parabola.&#10; ...

Question 40

Graph the parabola.&#10;

Accepted Answer

The answer of Graph the parabola.&#10; ...

Question 41

Give the focus, directrix, and axis for the parabola.
A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 10 m down from the top of the dome the ceiling is 19 m wide,
Find the best location for the light source.

A) 9 m down from the top
B) 4.6 m down from the top
C) 2.3 m down from the top
D) 6.9 m down from the top

Accepted Answer

The answer of Give the focus, directrix, and axis for...

Question 42

Give the focus, directrix, and axis for the parabola.&#10;

Accepted Answer

The answer of Give the focus, directrix, and axis for...

Question 43

Provide an appropriate response.&#10;Why is it not possible to choose h and k, neither zero, so the parabola   has its vertex at the origin?

Accepted Answer

The answer of Provide an appropriate response.&#10;Why is it not...

Question 44

Give the focus, directrix, and axis for the parabola.&#10;

Accepted Answer

The answer of Give the focus, directrix, and axis for...

Question 45

Give the focus, directrix, and axis for the parabola.&#10;

Accepted Answer

The answer of Give the focus, directrix, and axis for...

Question 46

Give the focus, directrix, and axis for the parabola.&#10;

Accepted Answer

The answer of Give the focus, directrix, and axis for...

Question 47

Give the focus, directrix, and axis for the parabola.
A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 10 m down from the top of the dome the ceiling is 19 m wide,
Find the best location for the light source.

A) 9 m down from the top
B) 4.6 m down from the top
C) 2.3 m down from the top
D) 6.9 m down from the top

Accepted Answer

The answer of Give the focus, directrix, and axis for...

Question 48

Give the focus, directrix, and axis for the parabola.&#10;

Accepted Answer

The answer of Give the focus, directrix, and axis for...

Question 49

Give the focus, directrix, and axis for the parabola.&#10;

Accepted Answer

The answer of Give the focus, directrix, and axis for...

Question 50

Give the focus, directrix, and axis for the parabola.&#10;

Accepted Answer

The answer of Give the focus, directrix, and axis for...

Question 51

Give the focus, directrix, and axis for the parabola.&#10;

Accepted Answer

The answer of Give the focus, directrix, and axis for...

Question 52

Give the focus, directrix, and axis for the parabola.
A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 10 m down from the top of the dome the ceiling is 19 m wide,
Find the best location for the light source.

A) 9 m down from the top
B) 4.6 m down from the top
C) 2.3 m down from the top
D) 6.9 m down from the top