Find the Vertex Form y=3/4x^2+9x

$y = \frac{3}{4} x^{2} + 9 x$

Step 1

Combine $\frac{3}{4}$ and $x^{2}$ .

$y = \frac{3 x^{2}}{4} + 9 x$

Step 2

Complete the square for $\frac{3 x^{2}}{4} + 9 x$ .

Use the form $a x^{2} + b x + c$ , to find the values of $a$ , $b$ , and $c$ .

$a = \frac{3}{4}$

$b = 9$

$c = 0$

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e$

Find the value of $d$ using the formula $d = \frac{b}{2 a}$ .

Substitute the values of $a$ and $b$ into the formula $d = \frac{b}{2 a}$ .

$d = \frac{9}{2 (\frac{3}{4})}$

Simplify the right side.

Combine $2$ and $\frac{3}{4}$ .

$d = \frac{9}{\frac{2 \cdot 3}{4}}$

Multiply $2$ by $3$ .

$d = \frac{9}{\frac{6}{4}}$

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6$ .

$d = \frac{9}{\frac{2 (3)}{4}}$

Cancel the common factors.

Factor $2$ out of $4$ .

$d = \frac{9}{\frac{2 \cdot 3}{2 \cdot 2}}$

Cancel the common factor.

$d = \frac{9}{\frac{2 \cdot 3}{2 \cdot 2}}$

Rewrite the expression.

$d = \frac{9}{\frac{3}{2}}$

Multiply the numerator by the reciprocal of the denominator.

$d = 9 (\frac{2}{3})$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$d = 3 (3) \frac{2}{3}$

Cancel the common factor.

$d = 3 \cdot 3 \frac{2}{3}$

Rewrite the expression.

$d = 3 \cdot 2$

Multiply $3$ by $2$ .

$d = 6$

Find the value of $e$ using the formula $e = c - \frac{b^{2}}{4 a}$ .

Substitute the values of $c$ , $b$ and $a$ into the formula $e = c - \frac{b^{2}}{4 a}$ .

$e = 0 - \frac{9^{2}}{4 (\frac{3}{4})}$

Simplify the right side.

Simplify each term.

Raise $9$ to the power of $2$ .

$e = 0 - \frac{81}{4 (\frac{3}{4})}$

Combine $4$ and $\frac{3}{4}$ .

$e = 0 - \frac{81}{\frac{4 \cdot 3}{4}}$

Multiply $4$ by $3$ .

$e = 0 - \frac{81}{\frac{12}{4}}$

Divide $12$ by $4$ .

$e = 0 - \frac{81}{3}$

Divide $81$ by $3$ .

$e = 0 - 1 \cdot 27$

Multiply $- 1$ by $27$ .

$e = 0 - 27$

Subtract $27$ from $0$ .

$e = - 27$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $\frac{3}{4} {(x + 6)}^{2} - 27$ .

$\frac{3}{4} {(x + 6)}^{2} - 27$

Step 3

Set $y$ equal to the new right side.

$y = \frac{3}{4} \cdot {(x + 6)}^{2} - 27$

Find the Vertex Form y=3/4x^2+9x

Related Questions

Support LCMGCF.com by disabling your adblocker.