Find the x and y Intercepts y=10-x^2+3x

$y = 10 - x^{2} + 3 x$

Find the x-intercepts.

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

$0 = 10 - x^{2} + 3 x$

Solve the equation.

Rewrite the equation as $10 - x^{2} + 3 x = 0$ .

$10 - x^{2} + 3 x = 0$

Factor the left side of the equation.

Factor $- 1$ out of $10 - x^{2} + 3 x$ .

Move $10$ .

$- x^{2} + 3 x + 10 = 0$

Factor $- 1$ out of $- x^{2}$ .

$- (x^{2}) + 3 x + 10 = 0$

Factor $- 1$ out of $3 x$ .

$- (x^{2}) - (- 3 x) + 10 = 0$

Rewrite $10$ as $- 1 (- 10)$ .

$- (x^{2}) - (- 3 x) - 1 \cdot - 10 = 0$

Factor $- 1$ out of $- (x^{2}) - (- 3 x)$ .

$- (x^{2} - 3 x) - 1 \cdot - 10 = 0$

Factor $- 1$ out of $- (x^{2} - 3 x) - 1 (- 10)$ .

$- (x^{2} - 3 x - 10) = 0$

Factor.

Factor $x^{2} - 3 x - 10$ using the AC method.

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 $- 10$ and whose sum is $- 3$ .

$- 5, 2$

Write the factored form using these integers.

$- ((x - 5) (x + 2)) = 0$

Remove unnecessary parentheses.

$- (x - 5) (x + 2) = 0$

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

$x - 5 = 0$

$x + 2 = 0$

Set $x - 5$ equal to $0$ and solve for $x$ .

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

The final solution is all the values that make $- (x - 5) (x + 2) = 0$ true.

$x = 5, - 2$

x-intercept(s) in point form.

x-intercept(s): $(5, 0), (- 2, 0)$

Find the y-intercepts.

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

$y = 10 - {(0)}^{2} + 3 (0)$

Solve the equation.

Remove parentheses.

$y = 10 - 0^{2} + 3 (0)$

Remove parentheses.

$y = 10 - {(0)}^{2} + 3 (0)$

Simplify $10 - {(0)}^{2} + 3 (0)$ .

Simplify each term.

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

$y = 10 - 0 + 3 (0)$

Multiply $- 1$ by $0$ .

$y = 10 + 0 + 3 (0)$

Multiply $3$ by $0$ .

$y = 10 + 0 + 0$

Simplify by adding numbers.

Add $10$ and $0$ .

$y = 10 + 0$

Add $10$ and $0$ .

$y = 10$

y-intercept(s) in point form.

y-intercept(s): $(0, 10)$

List the intersections.

x-intercept(s): $(5, 0), (- 2, 0)$

y-intercept(s): $(0, 10)$

Find the x and y Intercepts y=10-x^2+3x

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