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McGraw Hill Integrated II, 2012

MH

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

Practice makes perfect

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

P(x)= 0

0=- x^2+48x-512

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Write the terms on the LHS

LHS+x^2=RHS+x^2

x^2=48x-512

LHS-48x=RHS-48x

x^2-48x=-512

LHS+512=RHS+512

x^2-48x+512=0

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Factorize

Write as a sum

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

Factor out x

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

Factor out -32

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

Factor out (x-16)

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

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Solve using the Zero Product Property

Use the Zero Product Property

lx-16=0 x-32=0

(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.

Subchapter links

Exercises p.174-177