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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

1. Graphing Quadratic Functions

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Exercise 65 Page 101

Practice makes perfect

a

Since the equation gives the height of the ball after t seconds, to find the height of the ball after 1 second we will substitute 1 for t.

h=-16t^2+90t

t= 1

h=-16( 1)^2+90( 1)

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Simplify right-hand side

1^a=1

h=-16(1)+90(1)

a * 1=a

h=-16+90

Add terms

h=74

The height of the ball after 1 second is 74 feet.

b

To find the time when the ball is 126 feet high, we will first substitute 126 for h. Then, we will rewrite the equation in standard form.

h=-16t^2+90t

h= 126

126=-16t^2+90t

LHS+16t^2=RHS+16t^2

16t^2+126=90t

LHS-90t=RHS-90t

16t^2-90t+126=0

Next, we will solve the resulting equation for t by factoring. Notice that the GFC of the equation is 2, so we will first eliminate it. Let's start!

16t^2-90t+126=0

Factor out 2

2(8t^2-45t+63)=0

.LHS /2.=.RHS /2.

8t^2-45t+63=0

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Factor

Write as a difference

8t^2-21t-24t+63=0

Factor out t

t(8t-21)-24t+63=0

Factor out -3

t(8t-21)-3(8t-21)=0

Factor out (8t-21)

(8t-21)(t-3)=0

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Solve using the Zero Product Property

Use the Zero Product Property

lc8t-21=0 & (I) t-3=0 & (II)

(I): LHS+21=RHS+21

l8t=21 t-3=0

(I): .LHS /8.=.RHS /8.

lt=2.625 t-3=0

(II): LHS+3=RHS+3

lt=2.625 t=3

The ball is 126 feet high when t=2.625 and t=3.

c

Let's first substitute 0 for h in the equation and write the terms on the left-hand side.

h=-16t^2+90t

h= 0

0=-16t^2+90t

LHS+16t^2=RHS+16t^2

16t^2=90t

LHS-90t=RHS-90t

16t^2-90t=0

Next, we will solve the resulting equation for t by factoring out the GCF.

16t^2-90t=0

Factor out 2t

2t(8t-45)=0

▼

Solve using the Zero Product Property

Use the Zero Product Property

lc2t=0 & (I) 8t-45=0 & (II)

(I): .LHS /2.=.RHS /2.

lt=0 8t-45=0

(II): LHS+45=RHS+45

lt=0 8t=45

(II): .LHS /8.=.RHS /8.

lt=0 t=5.625

The height of 0 feet at t=0 represents that the ball was kicked from ground level. The height of 0 feet at t=5.625 represents the moment when the ball hits the ground.

Subchapter links

Exercises p.99-103