Precalculus Examples

$x = t + 2$ , $y = t^{2}$

Step 1

Set up the parametric equation for $x (t)$ to solve the equation for $t$ .

$x = t + 2$

Step 2

Rewrite the equation as $t + 2 = x$ .

$t + 2 = x$

Step 3

Subtract $2$ from both sides of the equation.

$t = x - 2$

Step 4

Replace $t$ in the equation for $y$ to get the equation in terms of $x$ .

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

Step 5

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

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Step 5.1

Rewrite ${(x - 2)}^{2}$ as $(x - 2) (x - 2)$ .

$y = (x - 2) (x - 2)$

Step 5.2

Expand $(x - 2) (x - 2)$ using the FOIL Method.

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Step 5.2.1

Apply the distributive property.

$y = x (x - 2) - 2 (x - 2)$

Step 5.2.2

Apply the distributive property.

$y = x \cdot x + x \cdot - 2 - 2 (x - 2)$

Step 5.2.3

Apply the distributive property.

$y = x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2$

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 $x$ by $x$ .

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

Step 5.3.1.2

Move $- 2$ to the left of $x$ .

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

Step 5.3.1.3

Multiply $- 2$ by $- 2$ .

$y = x^{2} - 2 x - 2 x + 4$

Step 5.3.2

Subtract $2 x$ from $- 2 x$ .

$y = x^{2} - 4 x + 4$