Question

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

y = –3(x + 2)2 + 10
y = –3(x – 2)2 + 10
y = –3(x + 2)2 – 14
y = –3(x – 2)2 – 2

Answer 1

A

Explanation:

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Answer 2

Option a

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

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=(2)/(3)`

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

`(b)/(2)= ((4)/(2)) = 2\\((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+(2)/(3)-4)`

Write the expression of the form

`-3(x+(b)/(2)) ^ 2 + (-3)(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