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Name:

Date:

Pre-Calculus 20

Unit 3

Quadratic Functions

Review Assignment

Mrs. Boughen

1. Sketch the graph of [pic] using points and symmetry, and determine the following:

a) the direction of the graph e) the domain

b) the width of the opening f) the range

c) the vertex g) the x-intercepts (show calculation)

d) the equation of the axis of symmetry h) the y-intercept (show calculation)

e) the max or min value i) the reflection point

[pic]

2. Sketch the graph of [pic] using transformations, and determine the following:

a) the direction of the graph e) the max or min. value

b) the width of the opening f) the domain

c) the vertex g) the range

d) the equation of the axis of symmetry h) the number of x-intercepts

[pic]

3. Determine a quadratic function in vertex form for each graph.

a) b)

[pic] [pic]

4. For the following quadratic function, identify the following:

a) the direction of opening e) the x-intercepts

b) the coordinates of the vertex f) the y-intercept

c) the maximum or minimum value g) the domain

d) the equation of the axis of symmetry h) the range

[pic]

5. A stone bridge has the shape of a parabolic arch, with a 40 ft width and 12 ft height.

a) Sketch and label a diagram to model this situation.

b) Determine the quadratic function to represent the shape of the arch.

c) What is the height of the arch at a width of 10 ft from the edge?

6. A projectile is fired out of a cannon at 105 m/s from a 100 m cliff. The function that models the height, h, of the trajectory in relation to time, t, is h(t) = –5t2 + 105t + 100.

a) Sketch the graph of the function with the help of the graphing calculator. Make sure to label the axes and the 3 important points. Use a ruler! Show your calculations for the vertex.

[pic]

b) What is the y-intercept of the function. What does the y-intercept represent?

c) What is the x-intercept of the function. What does the x-intercept represent?

d) What is the maximum height of the projectile and when does it occurs?

e) Determine the height of the projectile after 17.2 seconds in the air. Show calculations!

f) When does the projectile land on the ground?

g) Determine the domain and range that are appropriate for this situation.

7. Without graphing the function,[pic] determine the coordinates of the vertex algebraically. Show BOTH methods.

8. Use the method of Completing the Square to put the following functions in vertex form.

a) [pic] b) [pic]

c) [pic] d) [pic]

9. Consider the function: [pic].

a) Complete the Square to determine the maximum or minimum of the function.

b) Check your answer by using the formula for the x-coordinate of the vertex.

10. A window has the shape of a rectangle. The perimeter of the window is 12 m.

a) Write a function to approximate the area of the window as a function of its width.

b) Determine algebraically the maximum possible area of the window and the width that gives that area.

11. Two numbers have a sum of 46.

a) Write the function that models the maximum product of these numbers.

b) Determine algebraically the maximum product of the numbers and the value of the numbers that give this product.

12. You are a small business owner. You have determined that your profit, P, is a function of the number of items, n, you sell. The function that models your business situation is: [pic]. Determine algebraically how many items you have to sell to reach your maximum profit, and also determine what that maximum profit it.

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