SOLUTION: Find the vertex, line of symmetry, the maximum or minimum value of the quadratic equation, and graph the function. f(x)= -2x^2+2x+6

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Question 156941: Find the vertex, line of symmetry, the maximum or minimum value of the quadratic equation, and graph the function. f(x)= -2x^2+2x+6
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Find the vertex, line of symmetry, the maximum or minimum value of the quadratic equation, and graph the function. f(x)= -2x^2+2x+6
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set f(x) = 0 to find where it crosses the x-axis.
-2x^2+2x+6=0
x^2 - x - 3 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
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=13 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 2.30277563773199, -1.30277563773199. Here's your graph:

The vertex is at the minimum: set the 1st derivative to 0
2x-1=0
x = 1/2
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sub for x in the eqn
y = (1/4) - 1/2 - 3
y = -3 1/4 = -13/4
So the vertex is at (1/2,-13/4)
Since there's no xy term, the axis of symmetry is parallel to the y-axis. It goes thru the vertex, so it's:
x = 1/2

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