Algebra Examples

$C (t) = 2 (t - 4) (t + 1) (t - 6)$

Step 1

Find the x-intercepts.

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Step 1.1

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

$0 = 2 (x - 4) (x + 1) (x - 6)$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $2 (x - 4) (x + 1) (x - 6) = 0$ .

$2 (x - 4) (x + 1) (x - 6) = 0$

Step 1.2.2

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

$x - 4 = 0$

$x + 1 = 0$

$x - 6 = 0$

Step 1.2.3

Set $x - 4$ equal to $0$ and solve for $x$ .

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Step 1.2.3.1

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Step 1.2.3.2

Add $4$ to both sides of the equation.

$x = 4$

Step 1.2.4

Set $x + 1$ equal to $0$ and solve for $x$ .

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Step 1.2.4.1

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

$x + 1 = 0$

Step 1.2.4.2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 1.2.5

Set $x - 6$ equal to $0$ and solve for $x$ .

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Step 1.2.5.1

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Step 1.2.5.2

Add $6$ to both sides of the equation.

$x = 6$

Step 1.2.6

The final solution is all the values that make $2 (x - 4) (x + 1) (x - 6) = 0$ true.

$x = 4, - 1, 6$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(4, 0), (- 1, 0), (6, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

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

$y = 2 ((0) - 4) ((0) + 1) ((0) - 6)$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = 2 (0 - 4) ((0) + 1) ((0) - 6)$

Step 2.2.2

Remove parentheses.

$y = 2 (0 - 4) (0 + 1) ((0) - 6)$

Step 2.2.3

Remove parentheses.

$y = 2 (0 - 4) (0 + 1) (0 - 6)$

Step 2.2.4

Remove parentheses.

$y = 2 ((0) - 4) ((0) + 1) ((0) - 6)$

Step 2.2.5

Simplify $2 ((0) - 4) ((0) + 1) ((0) - 6)$ .

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Step 2.2.5.1

Subtract $4$ from $0$ .

$y = 2 \cdot - 4 ((0) + 1) ((0) - 6)$

Step 2.2.5.2

Multiply $2$ by $- 4$ .

$y = - 8 ((0) + 1) ((0) - 6)$

Step 2.2.5.3

Add $0$ and $1$ .

$y = - 8 \cdot 1 ((0) - 6)$

Step 2.2.5.4

Multiply $- 8$ by $1$ .

$y = - 8 ((0) - 6)$

Step 2.2.5.5

Subtract $6$ from $0$ .

$y = - 8 \cdot - 6$

Step 2.2.5.6

Multiply $- 8$ by $- 6$ .

$y = 48$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 48)$

Step 3

List the intersections.

x-intercept(s): $(4, 0), (- 1, 0), (6, 0)$

y-intercept(s): $(0, 48)$

Step 4