Name: ________________________ Class: ___________________ Date: __________ ID: A

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Algebra II - Chapter 5 Test 1 Review (3-6, 5-1 through 5-3)

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. Which is the graph of y 3(x 3)2 5?a. c.

b. d.

Name: ________________________ ID: A

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Short Answer

2. Graph y 2x 2 7.

3. Graph y x2 3x 2. Identify the vertex and the axis of symmetry.

Name: ________________________ ID: A

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4. Graph y (x 1)2 6.

5. In a baseball game, an outfielder throws a ball to the second baseman. The path of the ball is modeled by the

equation y 1

900 x 3752

2

70516 , where y is the height of the ball in feet after the ball has traveled x

feet horizontally. The second baseman catches the ball at the same height as the height at which the outfielder released it.a. What was the maximum height of the ball along its path? Answer to the nearest foot.b. How far was the second baseman from the outfielder at the time he caught the ball?c. How high above the ground was the ball when it left the hand of the outfielder?

6. Use the graph of y (x 3)2 5.a. If you translate the parabola to the right 2 units and down 7 units, what is the equation

of the new parabola in vertex form?b. If you translate the original parabola to the left 2 units and up 7 units, what is the

equation of the new parabola in vertex form?c. How could you translate the new parabola in part (a) to get the new parabola in part (b)?

Solve the system using either method of substitution or elimination.

7.

x y 2z 7

x 3y 4z 8

2x 2y 2z 0

8. Find a quadratic function to model the values in the table. Predict the value of y for x = 8.

x y

–1 3

0 2

3 35

Name: ________________________ ID: A

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Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.

9. y (x 4)(4x 4) 4x 2

Identify the vertex and the axis of symmetry of the parabola. Identify points corresponding to P and Q.

10.

11. A manufacturer determines that the number of drills it can sell is given by the formula

D 4p 2 152p 275, where p is the price of the drills in dollars.a. At what price will the manufacturer sell the maximum number of drills?b. What is the maximum number of drills that can be sold?

12. Use vertex form to write the equation of the parabola.

13. Identify the vertex and the y-intercept of the graph of the function y (x 2)2 5.

14. Write y 3x 2 18x 23 in vertex form.

Name: ________________________ ID: A

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Write the equation of the parabola in vertex form.

15. vertex (2, 3), point (–1, 48)

ID: A

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Algebra II - Chapter 5 Test 1 Review (3-6, 5-1 through 5-3)Answer Section

MULTIPLE CHOICE

1. ANS: D PTS: 1 DIF: L2 REF: 5-3 Translating ParabolasOBJ: 5-3.1 Using Vertex Form TOP: 5-3 Example 1 KEY: graphing | translation

SHORT ANSWER

2. ANS:

PTS: 1 DIF: L2 REF: 5-2 Properties of ParabolasOBJ: 5-2.1 Graphing Parabolas STA: PA 2.11.11.A | PA 2.8.11.RTOP: 5-2 Example 1 KEY: quadratic function | graphing

ID: A

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3. ANS:

vertex: 3

2,

1

4

, axis of symmetry: x

3

2

PTS: 1 DIF: L2 REF: 5-2 Properties of ParabolasOBJ: 5-2.1 Graphing Parabolas STA: PA 2.11.11.A | PA 2.8.11.RTOP: 5-2 Example 2 KEY: quadratic function | vertex of a parabola | axis of symmetry

4. ANS:

PTS: 1 DIF: L2 REF: 5-3 Translating ParabolasOBJ: 5-3.1 Using Vertex Form TOP: 5-3 Example 1 KEY: graphing | translation | parabola

ID: A

3

5. ANS: a. 44 ftb. 375 ftc. 5 ft

PTS: 1 DIF: L4 REF: 5-3 Translating ParabolasOBJ: 5-3.1 Using Vertex Form TOP: 5-3 Example 3 KEY: quadratic model | parabola | multi-part question | problem solving | word problem

6. ANS: a. y (x 5)2 2b. y (x 1)2 12c. left 4 units, up 14 units

PTS: 1 DIF: L3 REF: 5-3 Translating ParabolasOBJ: 5-3.1 Using Vertex Form TOP: 5-3 Example 2 KEY: parabola | translation | vertex form | problem solving | word problem | multi-part question

7. ANS: no solution

PTS: 1 DIF: L4 REF: 3-6 Systems With Three VariablesOBJ: 3-6.2 Solving Three-Variable Systems by Substitution STA: PA 2.8.11.HKEY: system with three variables | substitution method | solve by elimination

8. ANS:

y 3x 2 2x 2; 210

PTS: 1 DIF: L3 REF: 5-1 Modeling Data With Quadratic FunctionsOBJ: 5-1.2 Using Quadratic Models STA: PA 2.8.11.R TOP: 5-1 Example 3KEY: quadratic function | quadratic model

9. ANS: linear functionlinear term: 20xconstant term: 16

PTS: 1 DIF: L2 REF: 5-1 Modeling Data With Quadratic FunctionsOBJ: 5-1.1 Quadratic Functions and Their Graphs STA: PA 2.8.11.RTOP: 5-1 Example 1 KEY: quadratic function | quadratic term | linear term | constant term

10. ANS: (2, –2), x = 2P'(3, –1), Q'(0, 2)

PTS: 1 DIF: L2 REF: 5-1 Modeling Data With Quadratic FunctionsOBJ: 5-1.1 Quadratic Functions and Their Graphs STA: PA 2.8.11.RTOP: 5-1 Example 2 KEY: parabola | vertex of a parabola | axis of symmetry

ID: A

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11. ANS: $19; 1,169 drills

PTS: 1 DIF: L2 REF: 5-2 Properties of ParabolasOBJ: 5-2.2 Finding Maximum and Minimum Values STA: PA 2.11.11.A | PA 2.8.11.RTOP: 5-2 Example 4 KEY: maximum value | multi-part question | problem solving | word problem

12. ANS:

y (x 2)2 3

PTS: 1 DIF: L2 REF: 5-3 Translating ParabolasOBJ: 5-3.1 Using Vertex Form TOP: 5-3 Example 2 KEY: parabola | equation of a parabola | vertex form

13. ANS: vertex: (2, –5);y-intercept: –1

PTS: 1 DIF: L2 REF: 5-3 Translating ParabolasOBJ: 5-3.1 Using Vertex Form TOP: 5-3 Example 3 KEY: parabola | vertex of a parabola | y-intercept

14. ANS:

y 3(x 3)2 4

PTS: 1 DIF: L2 REF: 5-3 Translating ParabolasOBJ: 5-3.1 Using Vertex Form TOP: 5-3 Example 4 KEY: parabola | vertex form

15. ANS: y 5(x 2)2 3

PTS: 1 DIF: L3 REF: 5-3 Translating ParabolasOBJ: 5-3.1 Using Vertex Form TOP: 5-3 Example 2 KEY: parabola | equation of a parabola | vertex form