Question

3. What are the coordinates of the vertex of the graph of the function y = –3x² –12x + 3? (1 point

Answer 1

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

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

`-(b)/(2a)\\\\=(-(-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)

Answer 2

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)