Finite Math Examples

$- 25 x^{2} + 300 x$

Step 1

Write $- 25 x^{2} + 300 x$ as an equation.

$y = - 25 x^{2} + 300 x$

Step 2

Find the x-intercepts.

Tap for more steps...

Step 2.1

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

$0 = - 25 x^{2} + 300 x$

Step 2.2

Solve the equation.

Tap for more steps...

Step 2.2.1

Rewrite the equation as $- 25 x^{2} + 300 x = 0$ .

$- 25 x^{2} + 300 x = 0$

Step 2.2.2

Factor $- 25 x$ out of $- 25 x^{2} + 300 x$ .

Tap for more steps...

Step 2.2.2.1

Factor $- 25 x$ out of $- 25 x^{2}$ .

$- 25 x \cdot x + 300 x = 0$

Step 2.2.2.2

Factor $- 25 x$ out of $300 x$ .

$- 25 x \cdot x - 25 x \cdot - 12 = 0$

Step 2.2.2.3

Factor $- 25 x$ out of $- 25 x (x) - 25 x (- 12)$ .

$- 25 x (x - 12) = 0$

Step 2.2.3

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

$x = 0$

$x - 12 = 0$

Step 2.2.4

Set $x$ equal to $0$ .

$x = 0$

Step 2.2.5

Set $x - 12$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.2.5.1

Set $x - 12$ equal to $0$ .

$x - 12 = 0$

Step 2.2.5.2

Add $12$ to both sides of the equation.

$x = 12$

Step 2.2.6

The final solution is all the values that make $- 25 x (x - 12) = 0$ true.

$x = 0, 12$

Step 2.3

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (12, 0)$

Step 3

Find the y-intercepts.

Tap for more steps...

Step 3.1

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

$y = - 25 {(0)}^{2} + 300 (0)$

Step 3.2

Solve the equation.

Tap for more steps...

Step 3.2.1

Remove parentheses.

$y = - 25 \cdot 0^{2} + 300 (0)$

Step 3.2.2

Remove parentheses.

$y = - 25 {(0)}^{2} + 300 (0)$

Step 3.2.3

Simplify $- 25 {(0)}^{2} + 300 (0)$ .

Tap for more steps...

Step 3.2.3.1

Simplify each term.

Tap for more steps...

Step 3.2.3.1.1

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

$y = - 25 \cdot 0 + 300 (0)$

Step 3.2.3.1.2

Multiply $- 25$ by $0$ .

$y = 0 + 300 (0)$

Step 3.2.3.1.3

Multiply $300$ by $0$ .

$y = 0 + 0$

Step 3.2.3.2

Add $0$ and $0$ .

$y = 0$

Step 3.3

y-intercept(s) in point form.

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

Step 4

List the intersections.

x-intercept(s): $(0, 0), (12, 0)$

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

Step 5