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Calculus Examples

x = t + 7

$x = t + 7$ ,

y = t^{2}

$y = t^{2}$

Step 1

Set up the parametric equation for

x (t)

$x (t)$ to solve the equation for

t

$t$ .

x = t + 7

$x = t + 7$

Step 2

Rewrite the equation as

t + 7 = x

$t + 7 = x$ .

t + 7 = x

$t + 7 = x$

Step 3

Subtract

7

$7$ from both sides of the equation.

t = x - 7

$t = x - 7$

Step 4

Replace

t

$t$ in the equation for

y

$y$ to get the equation in terms of

x

$x$ .

y = {(x - 7)}^{2}

$y = {(x - 7)}^{2}$

Step 5

Simplify

{(x - 7)}^{2}

${(x - 7)}^{2}$ .

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Step 5.1

Rewrite

{(x - 7)}^{2}

${(x - 7)}^{2}$ as

(x - 7) (x - 7)

$(x - 7) (x - 7)$ .

y = (x - 7) (x - 7)

$y = (x - 7) (x - 7)$

Step 5.2

Expand

(x - 7) (x - 7)

$(x - 7) (x - 7)$ using the FOIL Method.

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Step 5.2.1

Apply the distributive property.

y = x (x - 7) - 7 (x - 7)

$y = x (x - 7) - 7 (x - 7)$

Step 5.2.2

Apply the distributive property.

y = x \cdot x + x \cdot - 7 - 7 (x - 7)

$y = x \cdot x + x \cdot - 7 - 7 (x - 7)$

Step 5.2.3

Apply the distributive property.

y = x \cdot x + x \cdot - 7 - 7 x - 7 \cdot - 7

$y = x \cdot x + x \cdot - 7 - 7 x - 7 \cdot - 7$

y = x \cdot x + x \cdot - 7 - 7 x - 7 \cdot - 7

$y = x \cdot x + x \cdot - 7 - 7 x - 7 \cdot - 7$

Step 5.3

Simplify and combine like terms.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Multiply

x

$x$ by

x

$x$ .

y = x^{2} + x \cdot - 7 - 7 x - 7 \cdot - 7

$y = x^{2} + x \cdot - 7 - 7 x - 7 \cdot - 7$

Step 5.3.1.2

Move

$- 7$ to the left of

$x$ .

$y = x^{2} - 7 \cdot x - 7 x - 7 \cdot - 7$

Step 5.3.1.3

Multiply

$- 7$ by

$- 7$ .

$y = x^{2} - 7 x - 7 x + 49$

$y = x^{2} - 7 x - 7 x + 49$

Step 5.3.2

Subtract

$7 x$ from

$- 7 x$ .

$y = x^{2} - 14 x + 49$

$y = x^{2} - 14 x + 49$

$y = x^{2} - 14 x + 49$

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