Answer:
Option a
[tex]-3(x+2) ^ 2 +10[/tex]
Step-by-step explanation:
If we have a quadratic equation
[tex]ax ^ 2 + bx + c[/tex]
Where a, b and are real coefficients of the equation, then to write the expression of the form:
[tex]a(x-h) ^ 2 + k[/tex]
we must use the square completion method.
In this problem we have the expression
[tex]y = -3x^2 - 12x - 2[/tex]
First take common factor -3.
[tex]y = -3(x^2 +4x +2/3)[/tex]
So
[tex]a = 1\\\\b=4\\\\c=\frac{2}{3}[/tex]
Second, divide b by 2. The result obtained square it
[tex]\frac{b}{2}= (\frac{4}{2}) = 2\\(\frac{b}{2})^2=2^2 = 4[/tex]
Now add and subtract from the right side of the equation the result obtained
[tex]y = -3(x^2 +4x +4+\frac{2}{3}-4)[/tex]
Write the expression of the form
[tex]-3(x+\frac{b}{2}) ^ 2 + (-3)\frac{2}{3} -4(-3)[/tex]
simplify
[tex]-3(x+2) ^ 2 -2 +12[/tex]
[tex]-3(x+2) ^ 2 +10[/tex]
So
[tex]y = -3x^2 - 12x - 2=-3(x+2) ^ 2 +10[/tex]
The answer is option a
