Find the Vertex Form 8x^2-8x+21

$8 x^{2} - 8 x + 21$

Write $8 x^{2} - 8 x + 21$ as an equation.

$y = 8 x^{2} - 8 x + 21$

Complete the square for $8 x^{2} - 8 x + 21$ .

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

$a = 8$

$b = - 8$

$c = 21$

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 $d = \frac{b}{2 a}$ .

$d = \frac{- 8}{2 \cdot 8}$

Simplify the right side.

Cancel the common factor of $- 8$ and $2$ .

Factor $2$ out of $- 8$ .

$d = \frac{2 \cdot - 4}{2 \cdot 8}$

Cancel the common factors.

Factor $2$ out of $2 \cdot 8$ .

$d = \frac{2 \cdot - 4}{2 (8)}$

Cancel the common factor.

$d = \frac{2 \cdot - 4}{2 \cdot 8}$

Rewrite the expression.

$d = \frac{- 4}{8}$

Cancel the common factor of $- 4$ and $8$ .

Factor $4$ out of $- 4$ .

$d = \frac{4 (- 1)}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$d = \frac{4 \cdot - 1}{4 \cdot 2}$

Cancel the common factor.

$d = \frac{4 \cdot - 1}{4 \cdot 2}$

Rewrite the expression.

$d = \frac{- 1}{2}$

Move the negative in front of the fraction.

$d = - \frac{1}{2}$

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 $e = c - \frac{b^{2}}{4 a}$ .

$e = 21 - \frac{{(- 8)}^{2}}{4 \cdot 8}$

Simplify the right side.

Simplify each term.

Cancel the common factor of ${(- 8)}^{2}$ and $8$ .

Rewrite $- 8$ as $- 1 (8)$ .

$e = 21 - \frac{{(- 1 (8))}^{2}}{4 \cdot 8}$

Apply the product rule to $- 1 (8)$ .

$e = 21 - \frac{{(- 1)}^{2} \cdot 8^{2}}{4 \cdot 8}$

Raise $- 1$ to the power of $2$ .

$e = 21 - \frac{1 \cdot 8^{2}}{4 \cdot 8}$

Multiply $8^{2}$ by $1$ .

$e = 21 - \frac{8^{2}}{4 \cdot 8}$

Factor $8$ out of $8^{2}$ .

$e = 21 - \frac{8 \cdot 8}{4 \cdot 8}$

Cancel the common factors.

Factor $8$ out of $4 \cdot 8$ .

$e = 21 - \frac{8 \cdot 8}{8 \cdot 4}$

Cancel the common factor.

$e = 21 - \frac{8 \cdot 8}{8 \cdot 4}$

Rewrite the expression.

$e = 21 - \frac{8}{4}$

Cancel the common factor of $8$ and $4$ .

Factor $4$ out of $8$ .

$e = 21 - \frac{4 \cdot 2}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$e = 21 - \frac{4 \cdot 2}{4 (1)}$

Cancel the common factor.

$e = 21 - \frac{4 \cdot 2}{4 \cdot 1}$

Rewrite the expression.

$e = 21 - \frac{2}{1}$

Divide $2$ by $1$ .

$e = 21 - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$e = 21 - 2$

Subtract $2$ from $21$ .

$e = 19$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $8 {(x - \frac{1}{2})}^{2} + 19$ .

$8 {(x - \frac{1}{2})}^{2} + 19$

Set $y$ equal to the new right side.

$y = 8 {(x - \frac{1}{2})}^{2} + 19$

Find the Vertex Form 8x^2-8x+21

Related Questions

Support LCMGCF.com by disabling your adblocker.