Question

consider the following parametric equations:

( x = sqrt { t + 4 } ) and ( y = 2 t + 5 )

step 1 of 2: eliminate the parameter ( t ). please write your answer in simplest form solved for ( y ).

Explanation:

Step1: Express \(t\) in terms of \(x\)

Given \(x = \sqrt{t + 4}\), square both sides: \(x^{2}=t + 4\), then \(t=x^{2}-4\).

Step2: Substitute \(t\) into the equation for \(y\)

Substitute \(t=x^{2}-4\) into \(y = 2t+5\). So \(y=2(x^{2}-4)+5\).

Step3: Simplify the equation

Expand \(y = 2(x^{2}-4)+5\): \(y=2x^{2}-8 + 5\). Then \(y=2x^{2}-3\). Since \(x=\sqrt{t + 4}\geq0\) (because the square root of a real - number \(t + 4\) is non - negative), the domain of \(x\) is \(x\geq0\).

Answer:

\(y = 2x^{2}-3,x\geq0\)