Question

Find the vertex of the parabola whose equation is y = x^2 + 8x + 12.

Answer 1

The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x 2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape.

The vertex of the parabola whose equation is y = x^2 + 8 x + 12 will be :
(x , y) = (-4,-4)

Answer 2

Answer:

The vertex of the parabola is (-4,-4).

Step-by-step explanation:

If a quadratic function is defined as

$y=ax^2+bx+c$              ... (1)

Then the vertex of the function is

$Vertex=(\frac{-b}{2a},f(\frac{-b}{2a}))$

The given function is

$y=x^2+8x+12$             .... (2)

From (1) and (2), we get a=1,b=8 and c=12.

$\frac{-b}{2a}=\frac{-8}{2(1)}=-4$

Substitute x=-4 in the given equation.

$f(\frac{-b}{2a})=f(-4)=y=(-4)^2+8(-4)+12$

$y=16-32+12=-4$

Therefore the vertex of the parabola is (-4,-4).