Question

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

Answer 1

Answer: the answer is C

Step-by-step explanation:

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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 $"12x"$ 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 $(h, k) = (- 6, -134)$