Find the x and y Intercepts y=5x^2-5

$y = 5 x^{2} - 5$

Step 1

Find the x-intercepts.

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

$0 = 5 x^{2} - 5$

Solve the equation.

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

$5 x^{2} - 5 = 0$

Add $5$ to both sides of the equation.

$5 x^{2} = 5$

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

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

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

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

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

Simplify the right side.

Divide $5$ by $5$ .

$x^{2} = 1$

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

$x = \pm \sqrt{1}$

Any root of $1$ is $1$ .

$x = \pm 1$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 1$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 1$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 1, - 1$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

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

Simplify each term.

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

$y = 5 \cdot 0 - 5$

Multiply $5$ by $0$ .

$y = 0 - 5$

Subtract $5$ from $0$ .

$y = - 5$

y-intercept(s) in point form.

y-intercept(s): $(0, - 5)$

Step 3

List the intersections.

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

y-intercept(s): $(0, - 5)$

Step 4

Find the x and y Intercepts y=5x^2-5

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