Trigonometry Examples

$f (x) = {(2 x + 5)}^{2}$

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 $x$ .

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

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as ${(2 x + 5)}^{2} = 0$ .

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

Step 1.2.2

Set the $2 x + 5$ equal to $0$ .

$2 x + 5 = 0$

Step 1.2.3

Solve for $x$ .

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Step 1.2.3.1

Subtract $5$ from both sides of the equation.

$2 x = - 5$

Step 1.2.3.2

Divide each term in $2 x = - 5$ by $2$ and simplify.

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Step 1.2.3.2.1

Divide each term in $2 x = - 5$ by $2$ .

$\frac{2 x}{2} = \frac{- 5}{2}$

Step 1.2.3.2.2

Simplify the left side.

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Step 1.2.3.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.3.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 5}{2}$

Step 1.2.3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 5}{2}$

Step 1.2.3.2.3

Simplify the right side.

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Step 1.2.3.2.3.1

Move the negative in front of the fraction.

$x = - \frac{5}{2}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- \frac{5}{2}, 0)$

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 $y$ .

$y = {(2 (0) + 5)}^{2}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = {(2 (0) + 5)}^{2}$

Step 2.2.2

Simplify ${(2 (0) + 5)}^{2}$ .

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Step 2.2.2.1

Multiply $2$ by $0$ .

$y = {(0 + 5)}^{2}$

Step 2.2.2.2

Add $0$ and $5$ .

$y = 5^{2}$

Step 2.2.2.3

Raise $5$ to the power of $2$ .

$y = 25$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 25)$

Step 3

List the intersections.

x-intercept(s): $(- \frac{5}{2}, 0)$

y-intercept(s): $(0, 25)$

Step 4