Question

The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown.

f(x) = 4(x2 + 12x) + 10

12/2^2 = 36

What is the function written in vertex form?

Answer 1

Answer: the answer is C

Explanation:

I took the test

Answer 2

Keywords:

Quadratic equation, vertex shape, parabola

For this case we have to rewrite the given quadratic equation, in the form of vertex, for this, we must take into account that a quadratic equation of the form
`ax ^ 2 + bx + c = 0`, can be rewritten in the form of vertex as:
`y = a (x-h) ^ 2 + k.` Vertice is the lowest or highest point of the parabola. The vertex is given by:
`(h, k)`. So, let:
`f (x) = 4x ^ 2 + 48x + 10`, to find the equation in the form of vertex, we follow the steps below:

Step 1:

We take the common factor to the first two terms of the equation:

`f (x) = 4 (x^2 + 12x) + 10`

Step 2:

We work square:

We divide the coefficient of the term
by 2 and its result is squared, that is:

`(\frac {12} {2}) ^ 2 = 36`

So, we have:

`f (x) = 4 (x^2 + 12x + 36-36) + 10`

Step 3:

We simplify:

`f (x) = 4 (x^2 + 12x + 36) + 10- (4 * 36)`

Step 4:

We factor:

`f (x) = 4 (x + 6) ^ 2-134`

Thus,
`h = -6\ and\ k = -134`

Answer:

The equation in the form of vertex is:
`f (x) = 4 (x + 6) ^ 2-134`, and the vertex is
`(h, k) = (- 6, -134)`