SOLUTION: f(x)=-x^2+12x+3 find the vertex(ordered pair): find line of symmetry: maximum/minimum of f(x) is: the value f(6)=39 is which of the following maximum or minimum:

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Question 259276: f(x)=-x^2+12x+3
find the vertex(ordered pair):
find line of symmetry:
maximum/minimum of f(x) is:
the value f(6)=39 is which of the following maximum or minimum:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=-x^2+12x+3
you seem to repeat yourself.
The vertex is the max/min. This one has a max at (6,39) which is f(6)=39
so that is three times you ask for the vertex and/or max
All parabolas are symmetric with respect to a line called the axis of symmetry. A parabola intersects its axis of symmetry at a point called the vertex of the parabola.
so that makes four times
The graph doesn't show it well but the peak (vertex is off to the right at 6,39
with x=6 the line of symmetry
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B12x%2B3+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2812%29%5E2-4%2A-1%2A3=156.

Discriminant d=156 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+156+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+156+%29%29%2F2%5C-1+=+-0.244997998398398
x%5B2%5D+=+%28-%2812%29-sqrt%28+156+%29%29%2F2%5C-1+=+12.2449979983984

Quadratic expression -1x%5E2%2B12x%2B3 can be factored:
-1x%5E2%2B12x%2B3+=+-1%28x--0.244997998398398%29%2A%28x-12.2449979983984%29
Again, the answer is: -0.244997998398398, 12.2449979983984. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B12%2Ax%2B3+%29