Algebra Examples

$y = x^{2} - 8 x + 7$

Find the x-intercepts.

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To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = x^{2} - 8 x + 7$

Solve the equation.

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Rewrite the equation as $x^{2} - 8 x + 7 = 0$ .

$x^{2} - 8 x + 7 = 0$

Factor $x^{2} - 8 x + 7$ using the AC method.

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Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $7$ and whose sum is $- 8$ .

$- 7, - 1$

Write the factored form using these integers.

$(x - 7) (x - 1) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 7 = 0$

$x - 1 = 0$

Set $x - 7$ equal to $0$ and solve for $x$ .

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Set $x - 7$ equal to $0$ .

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

Set $x - 1$ equal to $0$ and solve for $x$ .

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Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

The final solution is all the values that make $(x - 7) (x - 1) = 0$ true.

$x = 7, 1$

x-intercept(s) in point form.

x-intercept(s): $(7, 0), (1, 0)$

Find the y-intercepts.

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To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = {(0)}^{2} - 8 \cdot 0 + 7$

Solve the equation.

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Remove parentheses.

$y = 0^{2} - 8 \cdot 0 + 7$

Remove parentheses.

$y = {(0)}^{2} - 8 \cdot 0 + 7$

Simplify ${(0)}^{2} - 8 \cdot 0 + 7$ .

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Simplify each term.

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

$y = 0 - 8 \cdot 0 + 7$

Multiply $- 8$ by $0$ .

$y = 0 + 0 + 7$

Simplify by adding numbers.

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Add $0$ and $0$ .

$y = 0 + 7$

Add $0$ and $7$ .

$y = 7$

y-intercept(s) in point form.

y-intercept(s): $(0, 7)$

List the intersections.

x-intercept(s): $(7, 0), (1, 0)$

y-intercept(s): $(0, 7)$