Question

Which values for h and k are used to write the function f of x = x squared 12 x 6 in vertex form?

Answer 1

The values of h and k when f(x) = x^2 + 12x + 6 is in vertex form is -6 and -30

How to rewrite in vertex form?

The equation is given as:

f(x) = x^2 + 12x + 6

Rewrite as:

x^2 + 12x + 6 = 0

Subtract 6 from both sides

x^2 + 12x = -6

Take the coefficient of x

k = 12

Divide by 2

k/2 = 6

Square both sides

(k/2)^2 = 36

Add 36 to both sides of x^2 + 12x = -6

x^2 + 12x + 36= -6 + 36

Evaluate the sum

x^2 + 12x + 36= 30

Express as perfect square

(x + 6)^2 = 30

Subtract 30 from both sides

(x + 6)^2 -30 = 0

So, the equation f(x) = x^2 + 12x + 6 becomes

f(x) = (x + 6)^2 -30

A quadratic equation in vertex form is represented as:

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

Where:

Vertex = (h,k)

By comparison, we have:

(h,k) = (-6,-30)

Hence, the values of h and k when f(x) = x^2 + 12x + 6 is in vertex form is -6 and -30

Read more about quadratic functions at:

brainly.com/question/1214333

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