What is the vertex of the quadratic function f(x) = (x – 8)(x – 2)?
2 answers:
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
= = 5
Substitute x = 5 into f(x) for corresponding y- coordinate
f(5) = (5 - 8)(5 - 2) = (- 3)(3) = - 9
vertex = (5, - 9)
Answer: (5,-9)
Step-by-step explanation:
Make the multiplication indicated:
Add the like terms:
Now find the x-coordinate of the vertex with this formula:
In this case:
Then:
Rewrite the expression with
Now substitute into the function to find the y-coordinate of the vertex:
Therefore, the vertex is:
(5,-9)
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