Find the x and y Intercepts 6x^2-36x+30

$6 x^{2} - 36 x + 30$

Step 1

Write $6 x^{2} - 36 x + 30$ as an equation.

$y = 6 x^{2} - 36 x + 30$

Step 2

Find the x-intercepts.

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

$0 = 6 x^{2} - 36 x + 30$

Solve the equation.

Rewrite the equation as $6 x^{2} - 36 x + 30 = 0$ .

$6 x^{2} - 36 x + 30 = 0$

Factor the left side of the equation.

Factor $6$ out of $6 x^{2} - 36 x + 30$ .

Factor $6$ out of $6 x^{2}$ .

$6 (x^{2}) - 36 x + 30 = 0$

Factor $6$ out of $- 36 x$ .

$6 (x^{2}) + 6 (- 6 x) + 30 = 0$

Factor $6$ out of $30$ .

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

Factor $6$ out of $6 x^{2} + 6 (- 6 x)$ .

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

Factor $6$ out of $6 (x^{2} - 6 x) + 6 \cdot 5$ .

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

Factor.

Factor $x^{2} - 6 x + 5$ 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 $5$ and whose sum is $- 6$ .

$- 5, - 1$

Write the factored form using these integers.

$6 ((x - 5) (x - 1)) = 0$

Remove unnecessary parentheses.

$6 (x - 5) (x - 1) = 0$

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

$x - 5 = 0$

$x - 1 = 0$

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 $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

The final solution is all the values that make $6 (x - 5) (x - 1) = 0$ true.

$x = 5, 1$

x-intercept(s) in point form.

x-intercept(s): $(5, 0), (1, 0)$

Step 3

Find the y-intercepts.

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

$y = 6 {(0)}^{2} - 36 \cdot 0 + 30$

Solve the equation.

Remove parentheses.

$y = 6 \cdot 0^{2} - 36 \cdot 0 + 30$

Remove parentheses.

$y = 6 {(0)}^{2} - 36 \cdot 0 + 30$

Simplify $6 {(0)}^{2} - 36 \cdot 0 + 30$ .

Simplify each term.

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

$y = 6 \cdot 0 - 36 \cdot 0 + 30$

Multiply $6$ by $0$ .

$y = 0 - 36 \cdot 0 + 30$

Multiply $- 36$ by $0$ .

$y = 0 + 0 + 30$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 30$

Add $0$ and $30$ .

$y = 30$

y-intercept(s) in point form.

y-intercept(s): $(0, 30)$

Step 4

List the intersections.

x-intercept(s): $(5, 0), (1, 0)$

y-intercept(s): $(0, 30)$

Step 5

Find the x and y Intercepts 6x^2-36x+30

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