Question

How to find coordinates of vertex, and find out if the function has minimum or maximum value and find that value?

f(x)=2x^2+8x+9

&

f(x)=-x^2-2x+7

Please explain..I'm very lost. :(

Answer 1

you know the vertex of y=a(x-h)^2+k is at (h,k). The minimum value of (x-h) is zero, when x=h. For any other value of x, (x-h)^2 gets larger.

So, you want to get your function in that form and then you can just read off the coordinates of the vertex.

f(x) = 2x^2+8x+9
= 2(x^2+4x+4)+1
= 2(x+2)^2 + 1
So, the vertex is at (-2,1)

f(x) = -x^2-2x+7
= -(x^2+2x+1)+8
= -(x+1)^2+8
So the vertex is at (-1,8) and the parabola opens downward.

Answer 2

Thank you very much Steve.