Question

consider the following parametric equations: ( x = sqrt{t + 4} ) and ( y = 2t + 5 ) step 1 of 2: eliminate the parameter ( t ). please write your answer in simplest form solved for ( y ).

Explanation:

Step1: Solve for \(t\) from the equation 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 of \(y\)

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

Step3: Simplify the expression for \(y\)

Expand the right - hand side: \(y = 2x^{2}-8 + 5\). Then \(y=2x^{2}-3\). Also, note that since \(x=\sqrt{t + 4}\), \(x\geq0\).

Answer:

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