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Roman55 [17]
3 years ago
7

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

Mathematics
2 answers:
Anni [7]3 years ago
8 0

Answer:

(5, - 9)

Step-by-step 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} = \frac{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)

rodikova [14]3 years ago
3 0

Answer: (5,-9)

Step-by-step 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=\frac{-b}{2a}

In this case:

b=-10\\a=1

Then:

x=\frac{-(-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)

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