Lesson 9 Lining Up Quadratics Solidify Understanding

Ready

Multiply the following binomials using the open area models to assist you.

Example: $(2 x + 3) (5 x - 7)$

$= 10 x^{2} + x - 21$

1.

$(3 x - 4) (7 x - 5)$

2.

$(9 x + 2) (x + 6)$

3.

$(4 x - 3) (3 x + 11)$

4.

$(7 x + 3) (7 x - 3)$

5.

$(3 x - 10) (3 x + 10)$

6.

$(11 x + 5) (11 x - 5)$

7.

${(4 x + 5)}^{2}$

8.

${(x + 9)}^{2}$

9.

${(10 x - 7)}^{2}$

10.

The “like-term” boxes in the last three problems reveal a special pattern. Describe the relationship between the middle coefficient ( $b$ ) and the coefficients ( $a$ ) and ( $c$ ).

Set

Given the factored form of a quadratic function: Create the graph, and identify the vertex, intercepts, and vertical stretch of the parabola.

11.

$y = 4 (x - 2) (x + 6)$

Vertex:

$x$ -intercept(s):

$y$ -intercept:

Stretch:

12.

$y = - 3 (x + 2) (x - 6)$

Vertex:

$x$ -intercept(s):

$y$ -intercept:

Stretch:

13.

$y = (x + 5) (x + 7)$

Vertex:

$x$ -intercept(s):

$y$ -intercept:

Stretch:

14.

$y = \frac{1}{2} (x - 7) (x - 7)$

Vertex:

$x$ -intercept(s):

$y$ -intercept:

Stretch:

15.

$y = - \frac{1}{2} (x - 8) (x + 8)$

Vertex:

$x$ -intercept(s):

$y$ -intercept:

Stretch:

16.

$y = \frac{3}{5} (x - 25) (x - 9)$

Vertex:

$x$ -intercept(s):

$y$ -intercept:

Stretch:

Go

Given the vertex form of a quadratic function: Create the graph, and identify the vertex, intercepts, and vertical stretch of the parabola.

17.

$y = {(x + 2)}^{2} - 4$

Vertex:

$x$ -intercept(s):

$y$ -intercept:

Stretch:

18.

$y = - 3 {(x + 6)}^{2} + 3$

Vertex:

$x$ -intercept(s):

$y$ -intercept:

Stretch:

19.

$y = 2 {(x - 1)}^{2} - 8$

Vertex:

$x$ -intercept(s):

$y$ -intercept:

Stretch:

20.

Show the work that proves each of the following.

a.

$4 (x - 2) (x + 6) = 4 {(x + 2)}^{2} - 64$

b.

$- 3 (x + 2) (x - 6) = - 3 {(x - 2)}^{2} + 48$