Lesson 11 All Things Being Equal Develop Understanding

Ready

Find the features for each function represented with a graph.

1.

Graph shows the distance traveled during a family’s road trip.

Intervals of Increase:

Intervals of Decrease:

Maximum:

Minimum:

Domain:

Range:

2.

Graph shows actual and projected account balance for a charge account with today marked as day $0$ .

Intervals of Increase:

Intervals of Decrease:

Maximum:

Minimum:

Domain:

Range:

Set

Use the given graphs to find the vertex form of the equation. Use the equation to find the exact $x$ -intercepts.

3.

Vertex form of equation:

$x$ -intercepts:

4.

Vertex form of equation:

$x$ -intercepts:

5.

Vertex form of equation:

$x$ -intercepts:

6.

Vertex form of equation:

$x$ -intercepts:

Solve the following equations by factoring.

7.

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

8.

$x^{2} + 5 x + 6 = 0$

9.

$x^{2} + 8 x + 12 = 0$

10.

$x^{2} + 8 x + 15 = 0$

11.

$x^{2} - 3 x - 40 = 0$

12.

$x^{2} - 9 x - 36 = 0$

Go

Use the given functions to find the missing values. Graph each equation using technology to check your answers.

13.

$f (x) = x^{2} + 4 x - 12$

a.

$f (0) =$

b.

$f (2) =$

c.

$f (x) = 0, x =$

d.

$f (x) = 20, x =$

14.

$g (x) = {(x - 5)}^{2} + 2$

a.

$g (0) =$

b.

$g (5) =$

c.

$g (x) = 0, x =$

d.

$g (x) = 16, x =$

15.

$f (x) = x^{2} - 6 x + 9$

a.

$f (0) =$

b.

$f (- 3) =$

c.

$f (x) = 0, x =$

d.

$f (x) = 16, x =$

16.

$g (x) = {(x - 2)}^{2} - 3$

a.

$g (0) =$

b.

$g (5) =$

c.

$g (x) = 0, x =$

d.

$g (x) = - 3, x =$

17.

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

a.

$f (0) =$

b.

$f (- 2) =$

c.

$f (x) = 0, x =$

d.

$f (x) = 9, x =$

18.

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

a.

$g (0) =$

b.

$g (2) =$

c.

$g (x) = 0, x =$

d.

$g (x) = 4, x =$