SOLUTION: find the maximum y value on the graph of y=f(x). f(x)= -x^2+ 2x+ 6

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Question 763483: find the maximum y value on the graph of y=f(x).
f(x)= -x^2+ 2x+ 6
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=+-x%5E2%2B+2x%2B+6....since coefficient in front of x%5E2 is -1, parabola opens downward and the vertex is its maximum
write function in vertex form: y+=+a%28x-h%29%5E2%2Bk where h and k are coordinates of the vertex
y=+-x%5E2%2B+2x%2B+6.......complete the square, subtract 6 from both sides
y-6=+-x%5E2%2B+2x%2B+6-6
y-6=+-x%5E2%2B+2x ...factor out the leading coefficient -1
y-6=-1%28x%5E2-2x%29....take half of the x coefficient -2 to get -1, add and subtract
y-6=-1%28x%5E2-2x%2B1-1%29
y-6=-1%28%28x%5E2-2x%2B1%29-1%29
y-6=-1%28%28x-1%29%5E2-1%29
y-6=-%28x-1%29%5E2-%28-1%29
y-6=-%28x-1%29%5E2%2B1
y=-%28x-1%29%5E2%2B1%2B6
y=-%28x-1%29%5E2%2B7
Vertex: h+=+1, k+=7
so, the maximum y value on the graph is 7

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-%28x-1%29%5E2%2B7%29+