Eliminate the Parameter x=t+4 , y=t^2

$x = t + 4$ , $y = t^{2}$

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

$x = t + 4$

Rewrite the equation as $t + 4 = x$ .

$t + 4 = x$

Subtract $4$ from both sides of the equation.

$t = x - 4$

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

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

Simplify ${(x - 4)}^{2}$ .

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Rewrite ${(x - 4)}^{2}$ as $(x - 4) (x - 4)$ .

$y = (x - 4) (x - 4)$

Expand $(x - 4) (x - 4)$ using the FOIL Method.

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Apply the distributive property.

$y = x (x - 4) - 4 (x - 4)$

Apply the distributive property.

$y = x \cdot x + x \cdot - 4 - 4 (x - 4)$

Apply the distributive property.

$y = x \cdot x + x \cdot - 4 - 4 x - 4 \cdot - 4$

Simplify and combine like terms.

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Simplify each term.

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Multiply $x$ by $x$ .

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

Move $- 4$ to the left of $x$ .

$y = x^{2} - 4 \cdot x - 4 x - 4 \cdot - 4$

Multiply $- 4$ by $- 4$ .

$y = x^{2} - 4 x - 4 x + 16$

Subtract $4 x$ from $- 4 x$ .

$y = x^{2} - 8 x + 16$

Eliminate the Parameter x=t+4 , y=t^2

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