Exercise 83 Page 176

Begin by expanding the given equation.

See solution.

Practice makes perfect

Let's begin by expanding the given equation.

(x-p)(x-q)=0

Distr

Distribute (x-p)

x(x-p)-q(x-p)=0

Distr

Distribute x

x^2-px-q(x-p)=0

Distr

Distribute - q

x^2-px-qx+pq=0

SubTerm

Subtract term

x^2-(p+q)x+pq=0

Next, we will find the axis of symmetry by using the formula x= - b2a.

ax^2+ bx+ c ⇓ 1x^2 -(p+q)x+ pq In our case, a= 1 and b= -(p+q).

x=-b/2a

SubstituteII

a= 1, b= -(p+q)

x=--(p+q)/2( 1)

MoveNegNumToFrac

Put minus sign in front of fraction

x=p+q/2(1)

MultByOne

a * 1=a

x=p+q/2

We found the axis of symmetry. Now, we will find the midpoint between the x-intercepts p and q. To do that, we will add the x-intercepts and divide the sum by 2. Midpoint:p+q/2 As a result, the axis of symmetry passes through the midpoint of the x-intercepts p and q.

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Exercises p.174-177

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Exercise 83 Page 176

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