Question

What is the vertex of f(x)=2(x)^2+12(x)+16

Answer 1

The vertex of the quadratic function is -3, -2.

How to find the vertex of the quadratic function

The vertex form of a quadratic function f(x) = a(x - h)^2 + k can be found using the formula:

h = b/2a

k = f(h)

For the given quadratic function f(x) = 2x^2 + 12x + 16, the coefficients are:

a = 2

b = 12

c = 16

finding the x-coordinate of the vertex, h:

h =
`-(12)/(2(2)) = -(12)/(4) = -3`

Now, find the y-coordinate of the vertex, k, by substituting (x = -3) into the original function:

k =
`2(-3)^2 + 12(-3) + 16 = 2(9) - 36 + 16 = 18 - 36 + 16 = -2`

So, the vertex of the quadratic function is -3, -2.