SOLUTION: Write an equation in standard form of the parabola that has the same shape as the graph of f(x)= 4x^2 or g(x)=−4x2​, but with the given maximum or minimum. Maximum=7 at

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write an equation in standard form of the parabola that has the same shape as the graph of f(x)= 4x^2 or g(x)=−4x2​, but with the given maximum or minimum. Maximum=7 at       Log On


   



Question 1168800: Write an equation in standard form of the parabola that has the same shape as the graph of
f(x)= 4x^2 or
g(x)=−4x2​, but with the given maximum or minimum.
Maximum=7 at x=-2

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Write an equation in standard form of the parabola that has the same shape as the graph of
f%28x%29=+4x%5E2+ or g%28x%29=-4x%5E2​, but with the given maximum or minimum.

given:
Maximum=7 at x=-2 => vertex is at (-2,7)=(h,k) =>h=-2, k=7
To move a parabola h units to the right, you would substitute x-+h for x, and to move up ad k units in the corresponding quadratic equation
so, using g%28x%29=-4x%5E2
g%28x%29=-4%28x-h%29%5E2%2Bk where h=-2, k=7
The equation in a standard form of the parabola that has a maximum at f%28x%29+=+7+at x=-2 is
f%28x%29+=-+4%28x+-%28-+2%29%29%5E2+%2B7
f%28x%29+=+-4%28x+%2B2%29%5E2+%2B7