Algebra Examples

$v (w) = (60 - 4 w) w^{2}$

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 $x$ .

$0 = (60 - 4 x) \cdot x^{2}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $(60 - 4 x) \cdot x^{2} = 0$ .

$(60 - 4 x) \cdot x^{2} = 0$

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 $0$ .

$60 - 4 x = 0$

$x^{2} = 0$

Step 1.2.3

Set $60 - 4 x$ equal to $0$ and solve for $x$ .

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Step 1.2.3.1

Set $60 - 4 x$ equal to $0$ .

$60 - 4 x = 0$

Step 1.2.3.2

Solve $60 - 4 x = 0$ for $x$ .

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Step 1.2.3.2.1

Subtract $60$ from both sides of the equation.

$- 4 x = - 60$

Step 1.2.3.2.2

Divide each term in $- 4 x = - 60$ by $- 4$ and simplify.

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Step 1.2.3.2.2.1

Divide each term in $- 4 x = - 60$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 60}{- 4}$

Step 1.2.3.2.2.2

Simplify the left side.

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Step 1.2.3.2.2.2.1

Cancel the common factor of $- 4$ .

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Step 1.2.3.2.2.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 60}{- 4}$

Step 1.2.3.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 60}{- 4}$

Step 1.2.3.2.2.3

Simplify the right side.

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Step 1.2.3.2.2.3.1

Divide $- 60$ by $- 4$ .

$x = 15$

Step 1.2.4

Set $x^{2}$ equal to $0$ and solve for $x$ .

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Step 1.2.4.1

Set $x^{2}$ equal to $0$ .

$x^{2} = 0$

Step 1.2.4.2

Solve $x^{2} = 0$ for $x$ .

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Step 1.2.4.2.1

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

$x = \pm \sqrt{0}$

Step 1.2.4.2.2

Simplify $\pm \sqrt{0}$ .

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Step 1.2.4.2.2.1

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Step 1.2.4.2.2.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Step 1.2.4.2.2.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 1.2.5

The final solution is all the values that make $(60 - 4 x) \cdot x^{2} = 0$ true.

$x = 15, 0$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(15, 0), (0, 0)$

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 $y$ .

$y = (60 - 4 \cdot 0) {(0)}^{2}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = (60 - 4 \cdot 0) \cdot 0^{2}$

Step 2.2.2

Remove parentheses.

$y = (60 - 4 \cdot 0) {(0)}^{2}$

Step 2.2.3

Simplify $(60 - 4 \cdot 0) {(0)}^{2}$ .

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Step 2.2.3.1

Multiply $- 4$ by $0$ .

$y = (60 + 0) {(0)}^{2}$

Step 2.2.3.2

Add $60$ and $0$ .

$y = 60 {(0)}^{2}$

Step 2.2.3.3

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

$y = 60 \cdot 0$

Step 2.2.3.4

Multiply $60$ by $0$ .

$y = 0$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(15, 0), (0, 0)$

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

Step 4