Question

the function f(x) = x2 − 12x 5 written in vertex form is f(x) = (x − 6)2 − 31. what are the coordinates of the vertex? (6, 31) (−6, 31) (6, −31) (−6, −31)

Answer 1

f(x)=a(x-h)^2+k
vertex is (h,k)

f(x)=1(x-6)^2-31
f(x)=1(x-(6))^2+(-31)

h=6
k=-31
vertex=(6,-31)

Answer 2

The given function f(x) = x^2 − 12x 5 written in vertex form is f(x) = (x − 6)^2 − 31. Hence, The coordinates of the vertex is (6,-31).

What is the vertex form of a quadratic equation?

If a quadratic equation is written in the form

y = a(x - h)^2 + k

then it is called to be in vertex form.

It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)

This point (h,k) is called the vertex of the parabola that the quadratic equation represents.

The given function f(x) = x^2 − 12x 5 written in vertex form is f(x) = (x − 6)^2 − 31.

f(x)=a(x-h)^2+k

here, vertex is (h,k)

So,

$f(x) = 1(x-6)^2 - 31\\\\f(x) = 1(x-(6))^2 + (-31)$

The coordinates of the vertex is (h,k)

h = 6

k = -31

Hence, The coordinates of the vertex is (6,-31).

Learn more about the vertex form of a quadratic equation here:

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