body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Pearson Algebra 2 Common Core, 2011

PA

Pearson Algebra 2 Common Core, 2011 View details

4. Factoring Quadratic Expressions

Continue to next subchapter

Exercise 97 Page 223

a We are given the height of a baseball at certain times.

Time (s)	Height (ft)
$0.5$	$10$
$0.75$	$10.5$
$1$	$9$
$1.25$	$5.5$

To find the quadratic equation that models the ball's height we will use a graphing calculator. First, we have to enter the values into lists. Push $STAT$ , choose Edit, and then enter the values in the first two columns.

Now we will calculate a quadratic regression of this dataset. To view the quadratic regression analysis,we press $STAT$ , scroll to right to view the CALC options, and then choose the fifth option in the list, QuadReg.

Selecting Calculate calculates the values of the quadratic regression.

Using these values we can write an equation that models the height of the baseball depending on time.

h (t) = - 16 t^{2} + 22 t + 3

b We now have to factor the equation

h (t) = - 16 t^{2} + 22 t + 3 .

Since there are no common terms, we try to write

b t

as the sum of two terms with coefficients that are factors of

a c

and have a sum

b .

a c = - 16 \cdot 3 \Rightarrow a c = - 48

Since

a c = - 48 < 0,

the factors we are looking for have opposite signs. Because

b = 22 > 0,

the factor with greatest absolute value is positive.

Factors of $- 48$	Sum of Factors
$- 1, 48$	$47$
$- 2, 24$	$22$
$- 3, 16$	$13$
$- 4, 12$	$8$
$- 6, 8$	$2$

Using the factors

- 2

and

24,

we can rewrite the function.

- 16 t^{2} + 22 t + 3 = - 16 t^{2} 22 t - 2 t + 24 t + 3

Now we can factor the function.

- 16 t^{2} - 2 t + 24 t + 3

Factor out $- 2 t$

- 2 t (8 t + 1) + 24 t + 3

Factor out $3$

- 2 t (8 t + 1) + 3 (8 t + 1)

Factor out $(8 t + 1)$

(8 t + 1) (- 2 t + 3)

CommutativePropMult

Commutative Property of Multiplication

(- 2 t + 3) (8 t + 1)

FactorOutNegSignSwap

$a - b = - (b - a)$

- (2 t - 3) (8 t + 1)

Subchapter links

Lesson Check p.221

Practice and Problem-Solving Exercises p.221-223

Standardized Test Prep p.223

Mixed Review p.223