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Algebra Examples

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

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

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in

0

$0$ for

y

$y$ and solve for

x

$x$ .

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

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

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as

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

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

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

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

Step 1.2.2

Divide each term in

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

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

4

$4$ and simplify.

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Step 1.2.2.1

Divide each term in

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

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

4

$4$ .

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

$4$ .

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Step 1.2.2.2.1.1

Cancel the common factor.

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

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

Step 1.2.2.2.1.2

Divide

{(x - 3)}^{2}

${(x - 3)}^{2}$ by

1

$1$ .

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

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

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

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

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

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

Step 1.2.2.3

Simplify the right side.

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Step 1.2.2.3.1

Divide

0

$0$ by

4

$4$ .

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

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

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

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

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

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

Step 1.2.3

Set the

x - 3

$x - 3$ equal to

0

$0$ .

x - 3 = 0

$x - 3 = 0$

Step 1.2.4

Add

3

$3$ to both sides of the equation.

x = 3

$x = 3$

x = 3

$x = 3$

Step 1.3

x-intercept(s) in point form.

x-intercept(s):

(3, 0)

$(3, 0)$

x-intercept(s):

(3, 0)

$(3, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in

0

$0$ for

x

$x$ and solve for

y

$y$ .

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

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

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

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

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

Step 2.2.2

Remove parentheses.

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

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

Step 2.2.3

Simplify

4 {((0) - 3)}^{2}

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

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Step 2.2.3.1

Subtract

3

$3$ from

0

$0$ .

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

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

Step 2.2.3.2

Raise

- 3

$- 3$ to the power of

2

$2$ .

y = 4 \cdot 9

$y = 4 \cdot 9$

Step 2.2.3.3

Multiply

4

$4$ by

9

$9$ .

y = 36

$y = 36$

y = 36

$y = 36$

y = 36

$y = 36$

Step 2.3

y-intercept(s) in point form.

y-intercept(s):

(0, 36)

$(0, 36)$

y-intercept(s):

(0, 36)

$(0, 36)$

Step 3

List the intersections.

x-intercept(s):

(3, 0)

$(3, 0)$

y-intercept(s):

(0, 36)

$(0, 36)$

Step 4

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⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$