SOLUTION: Find the vertex of the parabola represented by the equation y=-2x^2+24x-100

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Question 647791: Find the vertex of the parabola represented by the equation y=-2x^2+24x-100
Answer by Algebraic(50) About Me  (Show Source):
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Remember that a quadratic equation can be derived from:
ax%5E2%2Bbx%2Bc
The equation you listed, y=-2x%5E2%2B24x-100 can be broken up into a, b, and c.
a = -2
b = 24
c = -100
To find the 'x' value of the vertex of a parabola, you must use the equation listed below:
x=-b%2F2a%29
Step 1: Replace the factors given with what is in the equation
x=-%2824%29%2F2%28-2%29%29
Step 2: Distribute the negative in front of the 24
x=-24%2F2%28-2%29%29
Step 3: Simplify
x=-24%2F-4
Step 4: Divide
x=6
The 'x' coordinate: x=6
To find the 'y' value of the vertex of a parabola, you must replace the 'x' coordinate into the original equation and solve.
Step 1: Replace the 'x' coordinate into the original equation
y=-2%286%29%5E2%2B24%286%29-100
Step 2: Simplify by using PEMDAS (order of operations)
y=-2%2836%29%2B24%286%29-100
Step 3: Continue simplifying
y=-72%2B144-100
Step 4: Continue simplifying
y=-28
Answer: The vertex to the parabola with the given equation is (6,-28)