Question

I have been working on these 2 problems and I think I am confusing myself. I have never tried this site before but it was recommended to me. I appreciate whoever can help me. Thanks in advance
The first question is
f(x)=-2x^2 + 2x + 8
I need to find the x and y coordinates of the vertex the line of symmetry and the max/min of f(x)
also the value of f(1/2) =17/2
The 2nd question has a fraction and I think this is confusing me on this one
f(x)=1/5(x+7)^2+7
I need to find the vertex line of symmetry max/min and is the value f(-7)=7 a minimum or a maximum?

Answer 1

-2x^2 + 2x + 8 = y
x^2 - x - 4 = -y/2
x^2 - x = -(1/2) y + 4
x^2 - x + 1/4 = -(1/2) y + 4 1/4
(x-1/2)^2 = -(2/4)y - 17/4
(x-1/2)^2 = -(2/4)(y - 8.5)
so
symmetric about the line x = 1/2
and the vertex is on that vertical line
at y = 8.5
so
vertex point = (1/2, 8.5)

LOL, we already know f(1/2) is 17/2 = 8.5

The parabola is upside down (sheds water , so the vertex is at the maximum.

Check that:
If x = 1/2 then
y = -2 (1/2)^2 +2(1/2) + 8
= -1/2 +1+8 = 8.5 check

Answer 2

can you help with the 2nd question? I have stressed myself over this and I am frustrated. I appreciate you help so much