Lesson 8 The Wow Factor Solidify Understanding

Ready

For each given quadratic equation:

graph the function,
state the vertex,
write the equation of the line of symmetry,
identify the stretch factor, and
indicate whether the quadratic has a maximum or a minimum.

1.

$f (x) = - 3 {(x + 5)}^{2} - 9$

Vertex:

Line of symmetry:

Stretch:

Maximum or Minimum:

2.

$f (x) = 2 x^{2} - 6 x + 7$

Vertex:

Line of symmetry:

Stretch:

Maximum or Minimum:

3.

$f (x) = - 4 x^{2} - 24 x + 20$

Vertex:

Line of symmetry:

Stretch:

Maximum or Minimum:

4.

$f (x) = 4 {(x - 2)}^{2} + 26$

Vertex:

Line of symmetry:

Stretch:

Maximum or Minimum:

Set

Write two equivalent expressions for the area represented by each block. Let $x$ be the side length of each of the large squares and $1$ be the side length of each of the small squares.

5.

6.

7.

8.

Each of the problems contains the same number of squares with the dimensions $x$ by $x$ and $1$ by $1$ , yet they are not the same size rectangle.

a.

What is different about them?

b.

How does this difference affect the expressions that represent the area?

c.

Describe how the arrangement of the squares and rectangles affects the factored form.

Another way to represent a quadratic expression is with an open area model. Each diagram represents both factored and standard form. For each open area model given, find the factored and standard form.

9.

10.

11.

Factor the following quadratic expressions. Use a visual model to assist you as needed.

12.

$4 x^{2} + 19 x - 5$

13.

$3 x^{2} - 10 x + 8$

14.

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

15.

$3 x^{2} - 14 x - 24$

16.

$2 x^{2} + 9 x + 10$

17.

$5 x^{2} + 31 x + 6$

18.

$5 x^{2} + 7 x - 6$

19.

$4 x^{2} + 8 x - 5$

Go

Given the $x$ -intercepts of a parabola, write the equation of the line of symmetry.

20.

$x$ -intercepts: $(- 3, 0)$ and $(3, 0)$

21.

$x$ -intercepts: $(- 4, 0)$ and $(16, 0)$

22.

$x$ -intercepts: $(- 2, 0)$ and $(5, 0)$

23.

$x$ -intercepts: $(- 14, 0)$ and $(- 3, 0)$

24.

$x$ -intercepts: $(17, 0)$ and $(33, 0)$

25.

$x$ -intercepts: $(- 0.75, 0)$ and $(2.25, 0)$