# SOLUTION: Find the vertex, and the x and y intercepts by completing the following: f(x) = -x^2 + 6x - 8

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Question 104962: Find the vertex, and the x and y intercepts by completing the following:
f(x) = -x^2 + 6x - 8

Answer by MathLover1(6611)   (Show Source):
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 Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form Start with the given equation Add to both sides Factor out the leading coefficient Take half of the x coefficient to get (ie ). Now square to get (ie ) Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of does not change the equation Now factor to get Distribute Multiply Now add to both sides to isolate y Combine like terms Now the quadratic is in vertex form where , , and . Remember (h,k) is the vertex and "a" is the stretch/compression factor. Check: Notice if we graph the original equation we get: Graph of . Notice how the vertex is (,). Notice if we graph the final equation we get: Graph of . Notice how the vertex is also (,). So if these two equations were graphed on the same coordinate plane, one would overlap another perfectly. So this visually verifies our answer.