Question 1

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

Accepted Answer

The equation is in the vertex form $y - k = a(x - h)^2$, where $(h, k)$ is the vertex. Here, $h = 15$ and $k = -10$, so the vertex is $(15, -10)$.

Question 2

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

Accepted Answer

B

Question 3

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

Accepted Answer

A parabola opening to the right with its vertex at the origin has the form $y^2 = 4px$. Substituting the point (4,3) into this equation, we get $3^2 = 4p(4)$, which simplifies to $9 = 16p$, giving $p = \frac{9}{16}$. Thus, the equation is $y^2 = \frac{9}{4}x$.

Question 4

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

Accepted Answer

The given equation is in the vertex form $y - k = a(x - h)^2$, where $(h, k)$ is the vertex of the parabola. Comparing, we find the vertex is $(6, 4)$.

Question 5

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

Accepted Answer

The equation is in the form $y = a - x^2 + bx + c$, where $a = -1$, indicating the parabola opens downward.

Question 6

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

Accepted Answer

The correct equation for a parabola opening downward with vertex at the origin is $x^2 = -4py$. Using the point (3, -6), we solve for $p$ and find that $p = \frac{3}{2}$, leading to $x^2 = -\frac{3}{2}y$.

Question 7

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 8

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

Accepted Answer

The equation is in the vertex form $y - k = a(x - h)^2$, where $(h, k)$ is the vertex. Here, $h = -4$ and $k = 13$, so the vertex is $(-4, 13)$.

Question 9

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

Accepted Answer

Since the parabola is symmetric with respect to the y-axis and has its vertex at the origin, it opens either up or down. The given point (9,9) suggests it opens upwards, fitting the form $x^2 = 4py$, where $p$ is the distance from the vertex to the focus. Substituting (9,9) into $x^2 = 4py$ gives $9^2 = 4p(9)$, solving for $p$ gives $p = 9/4$, but since the equation must work for any point on the parabola, not just (9,9), and considering the symmetry and direction of opening, the correct form is $x^2 = ky$, where $k$ is a constant. The correct equation that represents a parabola opening upwards with a vertex at the origin is $x^2 = 9y$, matching option A.

Question 10

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

Accepted Answer

The focus of a parabola with vertex at the origin and vertical axis is given by $(0, p)$, where $4p = 1/(a)$ in the equation $x^2 = 4py$. Given the focus $\left(0, -\frac{1}{17}\right)$, $p = -\frac{1}{17}$, so the equation is $x^2 = -\frac{4}{17}y$.

Question 11

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 12

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

Accepted Answer

The answer of Match the equation of 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

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 17

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 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

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

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

Write an equation for the parabola.&#10;

Accepted Answer

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

Question 24

Write an equation for the parabola.&#10;

Accepted Answer

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

Question 25

Graph the parabola.&#10;

Accepted Answer

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

Question 26

Graph the parabola.&#10;

Accepted Answer

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

Question 27

Graph the parabola.&#10;

Accepted Answer

The answer of Graph 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

Graph the parabola.&#10;

Accepted Answer

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

Question 31

Write an equation for the parabola.&#10;

Accepted Answer

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

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

Graph the parabola.&#10;

Accepted Answer

The answer of Graph 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

Write an equation for the parabola.&#10;

Accepted Answer

The answer of Write an equation for 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

Graph the parabola.&#10;

Accepted Answer

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

Question 39

Write an equation for the parabola.&#10;

Accepted Answer

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

Question 40

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 41

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

Accepted Answer

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

Question 42

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 43

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

Accepted Answer

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

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

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
Why is it not possible to choose h and k, neither zero, so the parabola f(x) = a(x - h)2 + k
has its vertex at the origin?

Accepted Answer

The answer of Write the word or phrase that best...

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.&#10;

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

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

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

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 52

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

Accepted Answer

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

Question 53

Write the word or phrase that best completes each statement or answers the question.&#10;Provide an appropriate response.&#10;Explain why the vertex of a parabola must lie on its axis.

Accepted Answer

The answer of Write the word or phrase that best...

Question 54

Solve the problem.&#10;A building has an entry the shape of a parabolic arch 4 ft high and 28 ft wide at the base. Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

Accepted Answer

The answer of Solve the problem.&#10;A building has an entry...

Question 55

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

Accepted Answer

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

Question 56

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

Accepted Answer

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

Question 57

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 58

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 59

Solve the problem.&#10;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 9 m down from the top of the dome the ceiling is 8 m wide,&#10;Find the best location for the light source.&#10;A) 1.8 m down from the top&#10;B) 0.4 m down from the top&#10;C) 1.2 m down from the top&#10;D) 0.8 m down from the top