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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

2. Solving Quadratic Equations by Graphing

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Exercise 31 Page 108

Rewrite the equation leaving all the terms on one side. Factor out the greatest common factor if it exists.

Number of x-intercepts: 1
x-intercept: - 2

Practice makes perfect

We want to find how many times times the graph of the given quadratic function intersects the x-axis and what are its zeros. To do that, we will substitute 0 for y and solve the resulting equation by factoring.

Factoring

Let's start by substituting y=0.

y=x^2+4x+4

y= 0

0=x^2+4x+4

Rearrange equation

x^2+4x+4=0

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Factor

SplitIntoFactors

Split into factors

x^2+2(2)x+4=0

CommutativePropMult

Commutative Property of Multiplication

x^2+2x(2)+4=0

Write as a power

x^2+2x(2)+2^2=0

FacPosPerfectSquare

a^2+2ab+b^2=(a+b)^2

(x+2)^2=0

Solving

To solve this equation, we will take square roots on both sides.

(x+2)^2=0

sqrt(LHS)=sqrt(RHS)

x+2=0

LHS-2=RHS-2

x=- 2

We found only one solution to the equation, which is x=- 2. Therefore, the graph of y=x^2+4x+4 intersects the x-axis once, at x=- 2.

Checking Our Answer

Checking our answer

We can substitute our solution back into the equation and simplify to check if our answer is correct.

x^2+4x+4=0

x= - 2

( - 2)^2+4( - 2)+4? =0

▼

Evaluate left-hand side

NegBaseToPosPow

(- a)^2 = a^2

4+4(- 2)+4? =0

a(- b)=- a * b

4+(- 8)+4? =0

a+(- b)=a-b

4-8+4? =0

Add and subtract terms

0=0 ✓

Substituting and simplifying created a true statement, so we know that x=- 2 is a solution of the equation.

Subchapter links

Exercises p.108-110