Verified Answer :

meerkat18

The function y = –3x² –12x + 3 is a parabola facing either upward of downward. we use completing the squares to find the vertex. 

y = -3(x² + 4x + 1) 

(k/2)^2 = (4/2)^2 = 4
y = -3(x² + 4x + 4 + 1 - 4) 

y = -3(x + 2)² + 9 
y- 9  = -3(x + 2)² 
vertex is equal to at (-2,9)

SociometricStar

Answer:

Vertex of the given function is (-2,15)

Step-by-step explanation:

The given equation is \(y=-3x^2-12x+3\)

It is a quadratic equation and we know that a quadratic equation represents a parabola. Hence, we find the vertex of the parabola.

The general equation of a quadratic equation is \(y=ax^2+bx+c\)

Comparing this equation with the given equation

a = -3, b = -12, c = 3

Now, the x coordinate of the vertex is

\(-\frac{b}{2a}\\\\=\frac{-(-12)}{2\cdot(-3)}\\\\=-2\)

Now, the y coordinate of the vertex is

\(y(-2)=-3(-2)^2-12(-2)+3\\\\=-12+24+3\\\\=15\)

Therefore, the vertex of the given function is (-2,15)

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