Lesson 12 Formula for Success Solidify Understanding

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1.

Find the $x$ -intercept of each equation. Write your answer as an ordered pair. Consider how the format of the given equation either facilitates or inhibits your work.

a.

$3 x + 4 y = 12$

b.

$y = 5 x - 3$

c.

$y - 5 = - 4 (x + 1)$

d.

$y = - 4 x + 1$

e.

$y - 6 = 2 (x + 7)$

f.

$5 x - 2 y = 10$

2.

Which form of the linear equations in problem 1 facilitates your work in finding $x$ -intercepts? Why?

3.

Using the same equations from problem 1, find the $y$ -intercepts. Write your answers as ordered pairs.

a.

$3 x + 4 y = 12$

b.

$y = 5 x - 3$

c.

$y - 5 = - 4 (x + 1)$

d.

$y = - 4 x + 1$

e.

$y - 6 = 2 (x + 7)$

f.

$5 x - 2 y = 10$

4.

Which of the formats above facilitate finding the $y$ -intercept? Why?

Set

Solve each of the quadratic equations using an appropriate method. Give a precise answer rather than an approximation.

5.

$x^{2} - 5 x - 7 = 0$

6.

$x^{2} + 15 x - 16 = 0$

7.

$x^{2} + 2 x - 35 = 0$

8.

$x^{2} + 9 x - 1 = 0$

9.

$- 2 x^{2} + 6 x + 7 = 0$

10.

$x^{2} + 7 x - 170 = 0$

11.

$x^{2} + 10 x - 80 = 0$

12.

$- 3 x^{2} - 6 x + 14 = 0$

13.

Which of the quadratic equations could have been solved by factoring more efficiently than by using the quadratic formula? How can you tell from the solutions?

Go

Write each of the expressions in factored form.

14.

$x^{2} - x - 132$

15.

$x^{2} - 5 x - 36$

16.

$x^{2} + 5 x + 6$

17.

$x^{2} + 13 x + 42$

18.

$x^{2} + x - 56$

19.

$x^{2} - x$

20.

$x^{2} - 8 x + 12$

21.

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

22.

$x^{2} + 5 x$