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What is the vertex of the quadratic function f(x) = (x – 8)(x – 2)?

User Ckunder
by
8.1k points

2 Answers

2 votes

Answer:

(5, - 9)

Explanation:

Given

f(x) = (x - 8)(x - 2) ← in factored form

Find the zeros by equating f(x) to zero, that is

(x - 8)(x - 2) = 0

Equate each factor to zero and solve for x

x - 8 = 0 ⇒ x = 8

x - 2 = 0 ⇒ x = 2

The vertex lies on the axis of symmetry which is located at the midpoint of the zeros, hence


x_(vertex) =
(8+2)/(2) = 5

Substitute x = 5 into f(x) for corresponding y- coordinate

f(5) = (5 - 8)(5 - 2) = (- 3)(3) = - 9

vertex = (5, - 9)

User Elifekiz
by
7.4k points
5 votes

Answer: (5,-9)

Explanation:

Make the multiplication indicated:


f(x) = x^2-2x-8x+16

Add the like terms:


f(x) = x^2-10x+16

Now find the x-coordinate of the vertex with this formula:


x=(-b)/(2a)

In this case:


b=-10\\a=1

Then:


x=(-(-10))/(2(1))=5

Rewrite the expression with
f(x)=y


y = x^2-10x+16

Now substitute
x=5 into the function to find the y-coordinate of the vertex:


y = (5)^2-10(5)+16


y =-9

Therefore, the vertex is:

(5,-9)

User Matt Aft
by
8.3k points

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