SOLUTION: Find the vertex, and the x and y intercepts by completing the following: f(x) = -x^2 + 6x - 8
-> SOLUTION: Find the vertex, and the x and y intercepts by completing the following: f(x) = -x^2 + 6x - 8
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Find the vertex, and the x and y intercepts by completing the following:
f(x) = -x^2 + 6x - 8
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Completing the Square to Get a Quadratic into Vertex Form
Start with the given equation
to both sides
Factor out the leading coefficient
Take half of the x coefficient
Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of
does not change the equation
to both sides to isolate y
Combine like terms
Now the quadratic is in vertex form
. Remember (h,k) is the vertex and "a" is the stretch/compression factor.
Notice if we graph the original equation
. Notice how the vertex is (
Notice if we graph the final equation
. 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.