Lesson 13 Comparison Shopping Practice Understanding

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1.

Find each absolute value.

a.

$| 7 |$

b.

$| - 3 |$

c.

$| 37 |$

d.

$| - 89 |$

2.

Find the value of each expression.

a.

$| - 3 + 7 |$

b.

$| 13 - 27 |$

c.

$| - 52 - 5 |$

d.

$| - 43 + 50 |$

3.

Find all values that satisfy the equation.

a.

$| x | = 6$

b.

$| x | = 92$

c.

$| x + 2 | = 15$

d.

$| x - 8 | = 10$

4.

What does absolute value mean? Can an absolute value ever be negative?

Set

For each of the quadratic equations, find the solutions using an efficient method. State the method you used.

5.

$x^{2} + 17 x + 60 = 0$

6.

$x^{2} + 16 x + 39 = 0$

7.

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

8.

$3 x^{2} + 14 x - 5 = 0$

9.

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

10.

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

Summarize the process for solving a quadratic equation by the indicated strategy. Give examples along with a written explanation; also indicate when it is best to use this strategy.

11.

Completing the square

12.

Factoring

13.

Quadratic formula

Two common strategies for solving systems of equations are graphing and substitution. In previous units, solving systems of linear equations has been done with these two methods. Use the same methods and apply them to the systems below.

For these systems, show how to solve algebraically and with a graph. You may use graphing technology if you desire.

14.

${\begin{cases} y = x^{2} + 5 x \\ y = 6 \end{cases}$

a.

Solve by substitution.

b.

Solve by graphing.

15.

${\begin{cases} y = x^{2} - 3 x - 10 \\ y = - 2 x + 10 \end{cases}$

a.

Solve by substitution.

b.

Solve by graphing.

Go

Graph the quadratic function and find the features indicated.

16.

$f (x) = x^{2} + 8 x + 13$

Line of symmetry:

$x$ -intercepts:

$y$ -intercept:

Vertex:

17.

$f (x) = x^{2} - 4 x - 1$

Line of symmetry:

$x$ -intercepts:

$y$ -intercept:

Vertex:

Solve each system of equations using an algebraic method.

18.

${\begin{cases} 3 x + 5 y = 15 \\ 3 x - 2 y = 6 \end{cases}$

19.

${\begin{cases} y = - 7 x + 12 \\ y = 5 x - 36 \end{cases}$

20.

${\begin{cases} y = 2 x + 12 \\ y = 10 x - x^{2} \end{cases}$

21.

${\begin{cases} y = 24 x - x^{2} \\ y = 8 x + 48 \end{cases}$

Find any missing labels for the diagrams, either side lengths or areas, and fill in any missing expressions in either factored or standard form of the quadratic equation.

22.

Factored form:

Standard form: $8 x^{2} + 14 x + 3$

23.

Factored form:

Standard form:

24.

Factored form: $(\underset{―}{} + 1) (\underset{―}{} - 4)$

Standard form: