Solve for a f(x)=a(x-h)^2+k

$f (x) = a {(x - h)}^{2} + k$

Step 1

Rewrite the equation as $a {(x - h)}^{2} + k = f (x)$ .

$a {(x - h)}^{2} + k = f (x)$

Step 2

Subtract $k$ from both sides of the equation.

$a {(x - h)}^{2} = f (x) - k$

Step 3

Divide each term in $a {(x - h)}^{2} = f (x) - k$ by ${(x - h)}^{2}$ and simplify.

Divide each term in $a {(x - h)}^{2} = f (x) - k$ by ${(x - h)}^{2}$ .

$\frac{a {(x - h)}^{2}}{{(x - h)}^{2}} = \frac{f (x)}{{(x - h)}^{2}} + \frac{- k}{{(x - h)}^{2}}$

Simplify the left side.

Cancel the common factor of ${(x - h)}^{2}$ .

Cancel the common factor.

$\frac{a {(x - h)}^{2}}{{(x - h)}^{2}} = \frac{f (x)}{{(x - h)}^{2}} + \frac{- k}{{(x - h)}^{2}}$

Divide $a$ by $1$ .

$a = \frac{f (x)}{{(x - h)}^{2}} + \frac{- k}{{(x - h)}^{2}}$

Simplify the right side.

Move the negative in front of the fraction.

$a = \frac{f (x)}{{(x - h)}^{2}} - \frac{k}{{(x - h)}^{2}}$