Chapter 7.5, Problem 29WE

To determine

The equation of the parabola in the form $y-k=a{\left(x-h\right)}^2$ after finding the value of $\left(a\right)$ if the equation of parabola is $y-3=a{\left(x-1\right)}^2$ which passes through the point $\left(2,5\right)$ .

Answer to Problem 29WE

The value of $a=2$ and the equation of the parabola is $y-3=2{\left(x-1\right)}^2$ .

Explanation of Solution

Given information: The equation of the given parabola is,

  $y-3=a{\left(x-1\right)}^2\mathrm{....}\left(1\right)$

Calculation: Since the parabola (1) passes through the point $\left(2,5\right)$ .Therefore satisfy point $\left(2,5\right)$ in (1) gives the value of $\left(a\right)$ . Therefore from (1),

  $\begin{array}{c}\left(5\right)-3=a{\left(\left(2\right)-1\right)}^2\mathrm{....}\left(\left(x,y\right)\to \left(2,5\right)\right)\\ 2=a\\ a=2\end{array}$

Again substitute $a=2$ in (1) will give the equation of the parabola. Therefore the equation of parabola from (1) is $y-3=2{\left(x-1\right)}^2$ .