SOLUTION: How do you complete this function equation f(x)=-2x^2+8x-5. I need to find the vertex h,k , compute h and k and graph the quadratic equation. Plus find the max value of f where it

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Question 204250: How do you complete this function equation f(x)=-2x^2+8x-5. I need to find the vertex h,k , compute h and k and graph the quadratic equation. Plus find the max value of f where it occurs.
I started the equation and found h.
a=-2 b=8 c=-5, so using the ormula -b/2a I got -8/2(-2) which gave me -8/-4 which gave me 2. h=2. Where do I go from here?
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
How do you complete this function equation f(x)=-2x^2+8x-5. I need to find the vertex h,k , compute h and k and graph the quadratic equation. Plus find the max value of f where it occurs.
I started the equation and found h.
a=-2 b=8 c=-5, so using the ormula -b/2a I got -8/2(-2) which gave me -8/-4 which gave me 2. h=2. Where do I go from here?
.
What you found:
-b/2a = 2
is the "axis of symmetry"
.
To find 'k', simply plug 2 back into the equation and solve:
f(x)=-2x^2+8x-5
f(2)=-2(2)^2+8(2)-5
f(x)=-8+16-5
f(x)=3
.
So, (h,k) = (2,3) vertex
.
To plot, looking at the 'a' coefficient (-2), we KNOW it is a parabola that opens downward. Use the "vertex" above and find two additional points to plot. The two additional points could be where the parabola crosses the x-axis:
0=-2x^2+8x-5
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=24 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.775255128608411, 3.22474487139159. Here's your graph:
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