Find the x and y Intercepts y^2=-6x+5

$y^{2} = - 6 x + 5$

Find the x-intercepts.

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

${(0)}^{2} = - 6 x + 5$

Solve the equation.

Rewrite the equation as $- 6 x + 5 = {(0)}^{2}$ .

$- 6 x + 5 = {(0)}^{2}$

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

$- 6 x + 5 = 0$

Subtract $5$ from both sides of the equation.

$- 6 x = - 5$

Divide each term in $- 6 x = - 5$ by $- 6$ and simplify.

Divide each term in $- 6 x = - 5$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 5}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 5}{- 6}$

Divide $x$ by $1$ .

$x = \frac{- 5}{- 6}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{5}{6}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{5}{6}, 0)$

Find the y-intercepts.

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

$y^{2} = - 6 \cdot 0 + 5$

Solve the equation.

Multiply $- 6$ by $0$ .

$y^{2} = 0 + 5$

Add $0$ and $5$ .

$y^{2} = 5$

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

$y = \pm \sqrt{5}$

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.

$y = \sqrt{5}$

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

$y = - \sqrt{5}$

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

$y = \sqrt{5}, - \sqrt{5}$

y-intercept(s) in point form.

y-intercept(s): $(0, \sqrt{5}), (0, - \sqrt{5})$

List the intersections.

x-intercept(s): $(\frac{5}{6}, 0)$

y-intercept(s): $(0, \sqrt{5}), (0, - \sqrt{5})$

Find the x and y Intercepts y^2=-6x+5

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