Question

Which equation is y = –3x2 – 12x – 2 rewritten in vertex form?

Answer 1

Answer:

Option a

$-3(x+2) ^ 2 +10$

Step-by-step explanation:

If we have a quadratic equation

$ax ^ 2 + bx + c$

Where a, b and are real coefficients of the equation, then to write the expression of the form:

$a(x-h) ^ 2 + k$

we must use the square completion method.

In this problem we have the expression

$y = -3x^2 - 12x - 2$

First take common factor -3.

$y = -3(x^2 +4x +2/3)$

So

$a = 1\\\\b=4\\\\c=\frac{2}{3}$

Second, divide b by 2. The result obtained square it

$\frac{b}{2}= (\frac{4}{2}) = 2\\(\frac{b}{2})^2=2^2 = 4$

Now add and subtract from the right side of the equation the result obtained

$y = -3(x^2 +4x +4+\frac{2}{3}-4)$

Write the expression of the form

$-3(x+\frac{b}{2}) ^ 2 + (-3)\frac{2}{3} -4(-3)$

simplify

$-3(x+2) ^ 2 -2 +12$

$-3(x+2) ^ 2 +10$

So

$y = -3x^2 - 12x - 2=-3(x+2) ^ 2 +10$

The answer is option a