Precalculus Examples

$f (x) = 4 {(x - 3)}^{2}$

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 $x$ .

$0 = 4 {(x - 3)}^{2}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $4 {(x - 3)}^{2} = 0$ .

$4 {(x - 3)}^{2} = 0$

Step 1.2.2

Divide each term in $4 {(x - 3)}^{2} = 0$ by $4$ and simplify.

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Step 1.2.2.1

Divide each term in $4 {(x - 3)}^{2} = 0$ by $4$ .

$\frac{4 {(x - 3)}^{2}}{4} = \frac{0}{4}$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Cancel the common factor of $4$ .

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Step 1.2.2.2.1.1

Cancel the common factor.

$\frac{4 {(x - 3)}^{2}}{4} = \frac{0}{4}$

Step 1.2.2.2.1.2

Divide ${(x - 3)}^{2}$ by $1$ .

${(x - 3)}^{2} = \frac{0}{4}$

Step 1.2.2.3

Simplify the right side.

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Step 1.2.2.3.1

Divide $0$ by $4$ .

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

Step 1.2.3

Set the $x - 3$ equal to $0$ .

$x - 3 = 0$

Step 1.2.4

Add $3$ to both sides of the equation.

$x = 3$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(3, 0)$

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 $y$ .

$y = 4 {((0) - 3)}^{2}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = 4 {(0 - 3)}^{2}$

Step 2.2.2

Remove parentheses.

$y = 4 {((0) - 3)}^{2}$

Step 2.2.3

Simplify $4 {((0) - 3)}^{2}$ .

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Step 2.2.3.1

Subtract $3$ from $0$ .

$y = 4 {(- 3)}^{2}$

Step 2.2.3.2

Raise $- 3$ to the power of $2$ .

$y = 4 \cdot 9$

Step 2.2.3.3

Multiply $4$ by $9$ .

$y = 36$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 36)$

Step 3

List the intersections.

x-intercept(s): $(3, 0)$

y-intercept(s): $(0, 36)$

Step 4

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