Lesson 7 Quadratic Quandaries Practice Understanding

Ready

Factor each quadratic expression completely.

1.

$x^{2} + x - 12$

2.

$x^{2} - 2 x - 8$

3.

$x^{2} + 5 x - 14$

4.

$4 x^{2} - 4 x - 24$

5.

$- x^{2} - 6 x - 9$

6.

$10 x^{2} - 70 x + 100$

7.

$10 x^{2} - 45 x - 25$

8.

$3 x^{2} - 3 x - 18$

9.

$2 x^{2} + 8 x - 42$

10.

How is the factored form of a quadratic function helpful when graphing the parabola?

Set

Solve each of the quadratic inequalities.

11.

$x^{2} + x - 12 > 0$

12.

$x^{2} - 2 x - 8 \leq 0$

13.

$x^{2} + 5 x - 14 \geq 0$

14.

$2 x^{2} - 9 x - 5 \geq 0$

15.

$3 x^{2} - 3 x - 18 < 0$

16.

$x^{2} + 4 x - 21 < 0$

17.

$x^{2} - 4 x \leq 0$

18.

$x^{2} \leq 25$

19.

$x^{2} - 4 x \leq 5$

20.

___
$y > x^{2} - x - 6$
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$y < x^{2} - 4$
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$y < (x + 2) (1 - x)$
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$y > 5 - 4 x - x^{2}$

Go

Write each quadratic function below in vertex form.

21.

$f (x) = x^{2} + 6 x + 5$

22.

$f (x) = (x + 3) (x - 5)$

23.

$f (x) = (x - 2) (x + 6)$

24.

$f (x) = x^{2} - 12 x + 20$

25.

$f (x) = 2 x^{2} + 16 x + 8$

26.

$f (x) = x^{2} - 2 x - 8$

Find the complex solutions for each equation.

27.

$x^{2} + 4 x + 5 = 0$

28.

$x^{2} + 2 x + 2 = 0$

29.

$x^{2} - 8 x + 20 = 0$