Algebra Examples

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

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = - 2 {(- 2)}^{2} + 8 (- 2)$

Step 2

Simplify $- 2 {(- 2)}^{2} + 8 (- 2)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $- 2$ by ${(- 2)}^{2}$ by adding the exponents.

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Step 2.1.1.1

Multiply $- 2$ by ${(- 2)}^{2}$ .

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Step 2.1.1.1.1

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

$y = {(- 2)}^{1} {(- 2)}^{2} + 8 (- 2)$

Step 2.1.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = {(- 2)}^{1 + 2} + 8 (- 2)$

Step 2.1.1.2

Add $1$ and $2$ .

$y = {(- 2)}^{3} + 8 (- 2)$

Step 2.1.2

Raise $- 2$ to the power of $3$ .

$y = - 8 + 8 (- 2)$

Step 2.1.3

Multiply $8$ by $- 2$ .

$y = - 8 - 16$

Step 2.2

Subtract $16$ from $- 8$ .

$y = - 24$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = - 2 {(- 1)}^{2} + 8 (- 1)$

Step 4

Simplify $- 2 {(- 1)}^{2} + 8 (- 1)$ .

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Step 4.1

Simplify each term.

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Step 4.1.1

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

$y = - 2 \cdot 1 + 8 (- 1)$

Step 4.1.2

Multiply $- 2$ by $1$ .

$y = - 2 + 8 (- 1)$

Step 4.1.3

Multiply $8$ by $- 1$ .

$y = - 2 - 8$

Step 4.2

Subtract $8$ from $- 2$ .

$y = - 10$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$y = - 2 {(0)}^{2} + 8 (0)$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = - 2 \cdot 0^{2} + 8 (0)$

Step 6.2

Remove parentheses.

$y = - 2 {(0)}^{2} + 8 (0)$

Step 6.3

Simplify $- 2 {(0)}^{2} + 8 (0)$ .

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Step 6.3.1

Simplify each term.

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Step 6.3.1.1

Raising $0$ to any positive power yields $0$ .

$y = - 2 \cdot 0 + 8 (0)$

Step 6.3.1.2

Multiply $- 2$ by $0$ .

$y = 0 + 8 (0)$

Step 6.3.1.3

Multiply $8$ by $0$ .

$y = 0 + 0$

Step 6.3.2

Add $0$ and $0$ .

$y = 0$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$y = - 2 {(1)}^{2} + 8 (1)$

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

$y = - 2 \cdot 1^{2} + 8 (1)$

Step 8.2

Remove parentheses.

$y = - 2 {(1)}^{2} + 8 (1)$

Step 8.3

Simplify $- 2 {(1)}^{2} + 8 (1)$ .

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Step 8.3.1

Simplify each term.

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Step 8.3.1.1

One to any power is one.

$y = - 2 \cdot 1 + 8 (1)$

Step 8.3.1.2

Multiply $- 2$ by $1$ .

$y = - 2 + 8 (1)$

Step 8.3.1.3

Multiply $8$ by $1$ .

$y = - 2 + 8$

Step 8.3.2

Add $- 2$ and $8$ .

$y = 6$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$y = - 2 {(2)}^{2} + 8 (2)$

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

$y = - 2 \cdot 2^{2} + 8 (2)$

Step 10.2

Remove parentheses.

$y = - 2 {(2)}^{2} + 8 (2)$

Step 10.3

Simplify $- 2 {(2)}^{2} + 8 (2)$ .

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Step 10.3.1

Simplify each term.

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Step 10.3.1.1

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

$y = - 2 \cdot 4 + 8 (2)$

Step 10.3.1.2

Multiply $- 2$ by $4$ .

$y = - 8 + 8 (2)$

Step 10.3.1.3

Multiply $8$ by $2$ .

$y = - 8 + 16$

Step 10.3.2

Add $- 8$ and $16$ .

$y = 8$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & - 24 \\ - 1 & - 10 \\ 0 & 0 \\ 1 & 6 \\ 2 & 8 \end{array}$

Step 12