Algebra Examples

$f (x) = 5 x^{2}$

Find the x-intercepts.

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

$0 = 5 x^{2}$

Solve the equation.

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Rewrite the equation as $5 x^{2} = 0$ .

$5 x^{2} = 0$

Divide each term in $5 x^{2} = 0$ by $5$ and simplify.

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Divide each term in $5 x^{2} = 0$ by $5$ .

$\frac{5 x^{2}}{5} = \frac{0}{5}$

Simplify the left side.

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Cancel the common factor of $5$ .

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Cancel the common factor.

$\frac{5 x^{2}}{5} = \frac{0}{5}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{0}{5}$

Simplify the right side.

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Divide $0$ by $5$ .

$x^{2} = 0$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

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Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

$y = 5 {(0)}^{2}$

Solve the equation.

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Remove parentheses.

$y = 5 \cdot 0^{2}$

Remove parentheses.

$y = 5 {(0)}^{2}$

Simplify $5 {(0)}^{2}$ .

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

$y = 5 \cdot 0$

Multiply $5$ by $0$ .

$y = 0$

y-intercept(s) in point form.

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

List the intersections.

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

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