Complete parts a-­c for each quadratic function.

a. Find the y­intercept, the equation of the axis of symmetry, and the x­ coordinates of the vertex.

b. Make a table of values that includes the vertex.

c. Use the information to graph the function.

1. f(x) = ­3x^2 + 8x

2. f(x) = 2x^2 + 7x + 1

Determine whether each function has a maximum or minimum value. State the maximum or minimum value of each function.

3. f(x) = x^2 + 6x + 9

4. f(x) = ­x^2 + 4x

5. Write a quadratic equation with roots ­3 and 4 in standard form.

Solve each quadratic equation using the method of your choice. Find exact solutions.

6. ­ 1.6x^2 ­- 3.2x + 18 = 0

7. 10x^2 + 3x = 1

8. x^2 + 8x ­ 48 = 0

Simplify the expression.

9. (5 ­- 2i) – (8 ­- 11i)

10. (14 -­ 5i)^2

Write each equation in vertex form. Then identify the vertex, axis of symmetry, and direction of opening.

11. y = x^2 + 10x + 27

12. y = ­9x^2 + 54x ­ 8

Graph each inequality.

13. (x ­- 5)(x + 7) < 0

14. ­ 5x^2 + x + 2 < 0

Find the exact solution to the system of equations. Check your answer algebraically.

15. y = x^2 ­- 6x + 1

y + 2x = 6

16. 2x^2 -­ 4x = y + 1

x + y = 1

 

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