Question

Find the vertex of the graph of the function.
f(x) = 4x^2 + 24x + 32

Answer 1

4x^2 + 24x + 32 = 4(x^2 + 6x + 8)
6/2 = 3 so:
= 4( (x+3)^2 - 3^2 + 8 )

= 4( (x+3)^2 - 9 + 8)

= 4( (x+3)^2 - 1)

= 4(x+3)^2 - 4

vertex will be the minimum point, so: now,

4(x+3)^2 - 4 is at a minimum when x = -3 because it makes the stuff being squared equal to 0 so we know the x cord of vertex
is -3 the y cord is the constant on the end, -4

Hope this helps