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McGraw Hill Integrated II, 2012 View details

1. Solving Quadratic Equations by Factoring

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Exercise 55 Page 175

To find the number of movie screens that produces profit, begin by finding the number of movie screens in which the profit is zero.

From 16 movie screens to 32 movie screens

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To find the number of movie screens that produces profit, we will begin by finding the number of movie screens in which the profit is zero.

P(x)=- x^2+48x-512

Substitute

P(x)= 0

0=- x^2+48x-512

▼

Write the terms on the LHS

AddEqn

LHS+x^2=RHS+x^2

x^2=48x-512

SubEqn

LHS-48x=RHS-48x

x^2-48x=-512

AddEqn

LHS+512=RHS+512

x^2-48x+512=0

▼

Factorize

WriteSum

Write as a sum

x^2-16x-32x+512=0

FactorOut

Factor out x

x(x-16)-32x+512=0

FactorOut

Factor out -32

x(x-16)-32(x-16)=0

FactorOut

Factor out (x-16)

(x-16)(x-32)=0

▼

Solve using the Zero Product Property

ZeroProdProp

Use the Zero Product Property

lx-16=0 x-32=0

AddEqn

(I): LHS+16=RHS+16

lx=16 x=32

When there are 16 or 32 movie screens, the profit is zero. Notice that the coefficient of the quadratic term is negative. This means that the graph of the function opens downward and it has a maximum value. Therefore, P(x) is non-negative for 16 ≤ x ≤ 32. When there are 16 to 32 screens, the company will not lose money.

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Exercises p.174-177

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101

102

103

Exercise 55 Page 175

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