Solve y=left(t-5right)^2-9

$$y= { \left(t-5 \right) }^{ 2 } -9$$

Solve for y

$$y=\left(t-8\right)\left(t-2\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(t-5\right)^{2}.

$$y=t^{2}-10t+25-9$$

Subtract 9 from 25 to get 16.

$$y=t^{2}-10t+16$$

Solve for t (complex solution)

$$t=-\sqrt{y+9}+5$$

$$t=\sqrt{y+9}+5$$

Solve for t

$$t=-\sqrt{y+9}+5$$

$$t=\sqrt{y+9}+5\text{, }y\geq -9$$