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Algebra I – Chapter 9 Test Review Standards/Goals:

A.CED.2.: I can write a quadratic function in standard form. E.2.a./F.IF.7.a.: I can recognize the graph of a quadratic function and understand the idea of

‘intercepts’ and minimum and maximum values. o I can find the domain and range of a quadratic function.

A.REI.4.a./E.1.c.: I can solve quadratic equations using the quadratic formula. E.2.a./F.IF.7.a.: I can identify solutions of quadratics based on its graph. A.REI.4.b./E.1.c.: I can solve quadratic equations using square roots. A.REI.4.a.: I can use the process of completing the square to transform a quadratic equation.

#1. Find the equation of the axis of symmetry and the coordinates of the vertex of the graph

of f(x) = 1

2(𝑥 − 6)2 + 8. Does the quadratic have a minimum or maximum value? Where is that

value?

#2. Find the coordinates of the vertex of the graph of f(x) = −6(𝑥 − 8)2 + 10. Identify the vertex as a maximum or a minimum. #3. Which of the following quadratics has a graph that is NARROWER?

6𝑥2 − 5 𝑂𝑅 1

6𝑥2 + 7𝑥 + 10

#4. Which value of ‘c’ makes the following trinomials a perfect square trinomial? a. 𝑥2 + 18𝑥 + 𝑐 b. 𝑥2 + 17𝑥 + 𝑐

#5. Find the y-intercept for: f(x) = −6(𝑥 − 8)2 + 10

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#6. Solve 𝑥2 − 12𝑥 − 8 = 2 by completing the square. Round to the nearest tenth, if necessary.

#7. Solve 4𝑥2 + 11𝑥 − 3 = 0 by using the Quadratic Formula. Round to the nearest tenth, if necessary.

#8. Solve 0 = 𝑥2 − 5.5𝑥 + 4 by using the Quadratic Formula. Round to the nearest tenth, if necessary.

#9. You want to enclose a rectangular area with 64 feet of fencing. What is the greatest possible area that you can enclose with the fence?

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#10. Describe how the graphs of 𝑦 = −4𝑥2 + 5𝑥 𝐴𝑁𝐷 𝑦 = 4𝑥2 + 5𝑥 will differ in appearance? #11. The graph of a quadratic function has x-intercepts at (-7,0) and (15,0). What values for ‘x’ would be ‘roots’ of this quadratic function? What is the vertex of each? Additionally, list the transformations for each quadratic. #12. 𝑦 = 4(𝑥 + 9)2 + 10 #13. 𝑦 = 4(𝑥 − 9)2 + 10

#14. 𝑦 = 14⁄ (𝑥 + 9)2 − 10 #15. 𝑦 = 1

4⁄ (𝑥 − 9)2 − 10

What is a solution for the following equations? #16. 𝑥2 + 21 = 102 #17. 𝑥2 + 100 = 0 #18. 𝑥2 − 100 = 0 #19. What is the side length of a square with an area of 64𝑦2?

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#20. The product of TWO consecutive integers, ‘n’ and ‘n + 1’ is 42. What is the positive integer that satisfies the situation? #21. MULTIPLE CHOICE QUESTION:

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Quadratics/Discriminant: FIRST: Find the discriminant of each and then state the number and type of roots that each will have. SECOND: Solve each using the quadratic formula: #22. 8𝑛2 − 4𝑛 = 18 #23. 8𝑎2 + 6𝑎 = −5 #24. Suppose the following was reflected across the x-axis. What would its equation be, after this reflection? 𝑦 = 𝑥2 + 9𝑥 − 17

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#25. The factored form of a quadratic is given by: f(x) = (x + w)(x +12). If f(x) has a y-intercept at (0,24), the value of ‘w’ must be: #26. What value for ‘w’ would result in |𝑥 + 8| + 𝑤 = 18 having no solution? #27. What value for ‘w’ would result in 𝑤|2𝑥 − 8| > 40 in having no solution? #28. What value for ‘w’ would result in 𝑥2 + 6𝑥 + 𝑤 in having NO REAL solutions? #29. What value for ‘w’ would result in 𝑥2 + 8𝑥 + 𝑤 in having ONE real solution? #30. Consider the following: 𝑓(𝑥) = −2𝑥2 + 16𝑥 − 8

a. What is the vertex of this quadratic? b. What is the axis of symmetry? c. What is the minimum or maximum value? d. What is the domain and range of this function? e. What is the y-intercept? f. What is the discriminant value and how many real solutions will it have?

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Find the discriminant of: #31. 𝑥2 − 5𝑥 + 9 = 0 #32. 3𝑥2 + 2𝑥 = 6 What is the vertex of the graphs shown below? Is each vertex a minimum or a maximum? State the axis of symmetry, y-intercept, domain and range of each. #33. #34. #35.

#36. Make a table of values. 𝒇(𝒙) = 𝟐𝒙𝟐 State the domain and range.

X Y

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#36. Make a table of values. 𝒇(𝒙) = 𝟐𝒙𝟐 + 𝒙 State the domain and range.

#37. MULTIPLE CHOICE QUESTION:

X Y

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