Precalculus Examples

$f (x) = - \frac{3}{4} + \frac{2}{5} {(x - 6)}^{2}$

Step 1

Isolate $y$ to the left side of the equation.

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Step 1.1

Simplify $- \frac{3}{4} + \frac{2}{5} {(x - 6)}^{2}$ .

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Step 1.1.1

Combine $\frac{2}{5}$ and ${(x - 6)}^{2}$ .

$y = - \frac{3}{4} + \frac{2 {(x - 6)}^{2}}{5}$

Step 1.1.2

Reorder $- \frac{3}{4}$ and $\frac{2 {(x - 6)}^{2}}{5}$ .

$y = \frac{2 {(x - 6)}^{2}}{5} - \frac{3}{4}$

Step 1.2

Reorder terms.

$y = \frac{2}{5} \cdot {(x - 6)}^{2} - \frac{3}{4}$

Step 2

Use the vertex form, $y = a {(x - h)}^{2} + k$ , to determine the values of $a$ , $h$ , and $k$ .

$a = \frac{2}{5}$

$h = 6$

$k = - \frac{3}{4}$

Step 3

Find the vertex $(h, k)$ .

$(6, - \frac{3}{4})$

Step 4