Algebra Examples

$y = x^{2} - 14 x + 49$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$x^{2} - 14 x + 49 = y$

Step 2

Subtract $49$ from both sides of the equation.

$x^{2} - 14 x = y - 49$

Step 3

Complete the square.

Tap for more steps...

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

$a = 1$

$b = - 14$

$c = 0 = y - 49$

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e = y - 49$

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

Tap for more steps...

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

$d = \frac{- 14}{2 \cdot 1}$

Cancel the common factor of $- 14$ and $2$ .

Tap for more steps...

Factor $2$ out of $- 14$ .

$d = \frac{2 \cdot - 7}{2 \cdot 1}$

Cancel the common factors.

Tap for more steps...

Factor $2$ out of $2 \cdot 1$ .

$d = \frac{2 \cdot - 7}{2 (1)}$

Cancel the common factor.

$d = \frac{2 \cdot - 7}{2 \cdot 1}$

Rewrite the expression.

$d = \frac{- 7}{1}$

Divide $- 7$ by $1$ .

$d = - 7$

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

Tap for more steps...

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

$e = 0 - \frac{{(- 14)}^{2}}{4 \cdot 1}$

Simplify the right side.

Tap for more steps...

Simplify each term.

Tap for more steps...

Raise $- 14$ to the power of $2$ .

$e = 0 - \frac{196}{4 \cdot 1}$

Multiply $4$ by $1$ .

$e = 0 - \frac{196}{4}$

Divide $196$ by $4$ .

$e = 0 - 1 \cdot 49$

Multiply $- 1$ by $49$ .

$e = 0 - 49$

Subtract $49$ from $0$ .

$e = - 49$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form ${(x - 7)}^{2} - 49$ .

${(x - 7)}^{2} - 49 = y - 49$

Step 4

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Add $49$ to both sides of the equation.

${(x - 7)}^{2} = y - 49 + 49$

Combine the opposite terms in $y - 49 + 49$ .

Tap for more steps...

Add $- 49$ and $49$ .

${(x - 7)}^{2} = y + 0$

Add $y$ and $0$ .

${(x - 7)}^{2} = y$