Chapter 7.5, Problem 27WE

To determine

The equation of the parabola in the form $y-k=a{\left(x-h\right)}^2$ after finding the value of $\left(h\right)$ if the equation of parabola is $y-8=3{\left(x-h\right)}^2$ and its axis is the line $x=5$ .

Answer to Problem 27WE

The value of $h=5$ and the equation of the parabola is $y-8=3{\left(x-5\right)}^2$ .

Explanation of Solution

Given information: The equation of the given parabola is,

  $y-8=3{\left(x-h\right)}^2\mathrm{....}\left(1\right)$

Calculation: Comparing (1) with $y-k=a{\left(x-h\right)}^2$ ,

Vertex of the parabola is $\left(h,8\right)\mathrm{....}\left(\text{2}\right)$

Now the axis of the parabola is the line $x=5$ , therefore $h=5$ because the axis of symmetry of parabola passes through the vertex of parabola.

Again substitute $h=5$ in (1) in the equation of the parabola. Therefore the equation of parabola from (1) is $y-8=3{\left(x-5\right)}^2$ .