Deck 8: Quadratics and the Mathematics of Motion

Question 1

Find coordinates of the focus of the parabola given by the equation

Answer 1

Question 2

Find a for the parabola , whose focus is located at

Answer 2

Question 3

The antenna is placed at the focus of a satellite dish. If the satellite has a 6-inch diameter and is 0.54 inches deep, how many inches from the vertex of the satellite dish should the antenna be placed?
Round your answer to 2 decimal places, if necessary.

Answer 3

4. 17 inches

Question 4

The light source is placed at the focus of a parabolic reflector. If the light source is 12.5 inches away from the reflector which is 2.88 inches deep, how many inches wide does the reflector need to be?
Round your answer to 2 decimal places, if necessary.

Question 5

Find for the function

Question 6

For the quadratic function pictured determine:

A) the coordinates of its vertex,
B) the equation of the axis of symmetry,
C) the x-coordinates of its horizontal intercepts (enter the values in numerical order separated by a comma), and
D) whether the parabola is concave up or concave down (enter up or down).

Question 7

For the quadratic function pictured determine the coordinates of its vertex.

Question 8

For the quadratic function pictured determine the equation of the axis of symmetry.

Question 9

For the quadratic function pictured determine the x-coordinates of its horizontal intercepts.
(Enter the values in numerical order separated by a comma.)

Question 10

For the quadratic function pictured determine whether the parabola is concave up or concave down.

A) down
B) up

Question 11

Using the quadratic function , fill in the values in the table.

Question 12

Given the point (2, 20) on a parabola of the form , find the equation of the parabola.

Question 13

Specify whether the vertex of this parabola is a maximum or a minimum.

A) Maximum
B) Minimum

Question 14

Determine whether this parabola is concave up or down.

A) Down
B) Up

Question 15

Put the quadratic into standard form:

Question 16

Find the equation, in standard form, of the parabola with horizontal intercepts at -5 and 1.

Question 17

Find the focus of a parabola represented by the equation with vertex at (-1, -4).

Question 18

Find the focus of a parabola represented by the equation with vertex at (4, -4).

Question 19

Select the equation whose graph is the graph of vertically compressed by a factor of 0.5.

A)
B)
C)
D)

Question 20

Select the choice which best describes the graph of .

A) It is the graph of shifted 0.6 units up.
B) It is the graph of vertically compressed by a factor of 0.6.
C) It is the graph of shifted 0.6 units to the left.
D) It is the graph of vertically compressed by a factor of 0.6 and reflected across the x-axis.

Question 21

Select the equation whose graph is the graph of vertically compressed by a factor of and reflected across the x-axis.

A)
B)
C)
D)

Question 22

Select the choice which best describes the graph of .

A) It is the graph of shifted 0.4 units to the right.
B) It is the graph of vertically compressed by a factor of 0.4.
C) It is the graph of shifted 0.4 units up.
D) It is the graph of vertically compressed by a factor of 0.4 and reflected across the x-axis.

Question 23

Select the equation whose graph is the graph of shifted 5 units up.

A)
B)
C)
D)

Question 24

Select the choice which best describes the graph of .

A) It is the graph of shifted 12 units up.
B) It is the graph of vertically stretched by a factor of 12.
C) It is the graph of shifted 12 units to the left.
D) It is the graph of shifted 12 units down.

Question 25

Select the equation whose graph is the graph of shifted 5 units to the right.

A)
B)
C)
D)

Question 26

Select the choice which best describes the graph of .

A) It is the graph of shifted 5 units to the right.
B) It is the graph of vertically stretched by a factor of 5.
C) It is the graph of shifted 5 units down.
D) It is the graph of shifted 5 units to the left.

Question 27

Transform the function into a new function by compressing by a factor of 0.2, reflecting across the x-axis, and then shifting the result down 3 units. Find the equation of

Question 28

Transform the function into a new function by stretching by a factor of 3 and reflecting across the x-axis, and then shifting the result down 3 units. Find the equation of .

Question 29

Transform the function into a new function by shifting horizontally 11 units to the right and then shifting the result up 4 units. Find the equation of

Question 30

Transform the function into a new function by shifting horizontally 5 units to the left, reflecting the result across the x-axis, and then shifting the result down 4 units. Find the equation of .

Question 31

Find the coordinates of the vertex of

Question 32

For the function , state whether the vertex represents a minimum or a maximum of the function.

A) minimum
B) maximum

Question 33

For the function ,

A) find the coordinates of the vertex and
B) state whether it represents a minimum or a maximum of the function (enter minimum or maximum)

Question 34

Select the equation that best describes the graph.

A)
B)
C)
D)

Question 35

Select the equation that best describes the graph.

A)
B)
C)
D)

Question 36

Create a quadratic equation of the form , where a = 0.5 and (h, k) = (-1, -7).

Question 37

Find the equation (in form) of a parabola with vertex of (-8, -4) that passes through the point (-4, 108).

Question 38

Convert the function into vertex form, , by completing the square.

Question 39

Convert the function into standard form,

Question 40

Find values for A and B using what you know about completing the square.

Question 41

Find values for A and B using what you know about completing the square.

Question 42

Find values for A and B using what you know about completing the square.

Question 43

Find values for A and B using what you know about completing the square. \

Question 44

Convert the function into vertex form, , by completing the square.

Question 45

Convert the function into vertex form, by completing the square.

Question 46

Convert the function into vertex form, .

Question 47

Find the coordinates of the vertex of the parabola given by . Give your answer as a reduced fraction or whole number.

Question 48

Find the x-coordinate of the vertex of the parabola given by . Give your answer as a reduced fraction or whole number.

Question 49

Find the coordinates of the vertex of the parabola given by . Round values to 2 decimal places, if necessary.

Question 50

Find a quadratic function, , that has vertex and . Write your answer in standard form .

Question 51

Find a formula for a parabola with vertex that passes through the point .Write your answer in standard form .

Question 52

Find the minimum value of the function . Round values to 2 decimal places, if necessary.

Question 53

The height, h, of a toy rocket t seconds after launch is given by the function .

A) Find the time (in seconds) when the rocket reaches the maximum height.
B) Find the maximum height (in feet) of the rocket.Round values to 2 decimal places, if necessary.

Question 54

The daily profit (f), in dollars, of a small business is given by the function, , where x represents the total number of units sold. What is the maximum daily profit of the business?

Question 55

The daily profit (f), in dollars, of a small business is given by the function, , where x represents the total number of units sold. How many units does the business need to sell in order to maximize the daily profit?

Question 56

Find the vertex of the parabola

Question 57

Find the vertex of the parabola

Question 58

Find two different equations; one where a = 4 and one where a = 5; for a parabola that goes through the points (1, 1) and (9, 1). Write the function in form.

Question 59

Write the equation, in form, for the graph

Question 60

Write the function in factored form, with .

Question 61

Write the function in factored form, with

Question 62

Find the horizontal intercepts of the function .
Write your answer as r₁, r₂, with r₁2.

Question 63

Find the horizontal intercepts of the function . Give exact answers. Write your answer as r₁, r₂, with r₁2.

Question 64

Find the horizontal intercepts of the function . Give exact answers. Write your answer as r₁, r₂, with r₁2.

Question 65

Find the horizontal intercepts of the function . Round answers to 2 decimal places, if necessary. Write your answer as r₁, r₂, with r₁2.

Question 66

Use the discriminant to determine how many real roots the function has.

A) 1
B) 2
C) 0

Question 67

Which of the following is true for the quadratic function whose graph is shown?

A) the discriminant is negative
B) the discriminant is zero
C) the discriminant is positive

Question 68

Find any solutions to the equation Write your answer as r₁, r₂, with r₁2. For complex answers enter .

Question 69

Find any solutions to the equation Write your answer as r₁, r₂, with r₁2. For complex answers enter .

Question 70

Find any solutions to the equation . Give exact answers.Write your answer as r₁, r₂, with r₁2. For complex answers enter .

Question 71

Find any solutions to the equation . Round answers to 2 decimal places Write your answer as r₁, r₂, with r₁2. For complex answers enter

Question 72

Find any solutions to the equation Write your answer as r₁, r₂, with r₁2. For complex answers enter .

Question 73

Find any solutions to the equation Write your answer as r₁, r₂, with r₁2. For complex answers enter .

Question 74

Find any solutions to the equation . Give exact answers. Write your answer as r₁, r₂, with r₁2. For complex answers enter .

Question 75

Find the quadratic function with x-intercepts -5 and -2 and y-intercept 30. Write your answer in standard form .

Question 76

Find the quadratic function with x-intercepts -5 and 7 such that . Write your answer in standard form .

Question 77

Write the function in factored form, .
Write the values for r₁ and r₂ in ascending order (r₁2.)

Question 78

Write the function in factored form, . Write the values for r₁ and r₂ in ascending order (r₁2.) For complex answers enter .

Question 79

Write the function in factored form, . Write the values for r₁ and r₂ in ascending order (r₁2.) For complex answers enter .

Question 80

For the following function, will the vertex be above, below, or on the x-axis?

A) Below
B) On
C) Above