Chapter 8.4, Problem 60E

To determine

To write: The quadratic function in vertex form whose graph has vertex at $(1,8)$ and passes through the point $(3,12)$ .

Answer to Problem 60E

  $y={(x-1)}^2+8$

Explanation of Solution

Given information:The function has vertex at $(1,8)$ and passes through the point $(3,12)$ .

Calculation:The vertex form of a quadratic function is represented as $y=a{(x-h)}^2+k$ where $(h,k)$ is the vertex and a is a constant.

Then, a quadratic function with vertex at $(1,8)$ is written as,

  $y=a{(x-1)}^2+8$ ...........(1)

Now, (1) passes through the point $(3,12)$ .

Then, $y=a{(x-1)}^2+8$

  $\begin{array}{l}\Rightarrow 12=a\cdot 2^2+8\\ \Rightarrow 12=4a+8\\ \Rightarrow 4a=12-8\\ \Rightarrow 4a=4\\ \Rightarrow a=1\end{array}$

Then, (1) becomes,

  $y={(x-1)}^2+8$

Thus, the function with vertex at $(1,8)$ and passing through the point $(3,12)$ is $y={(x-1)}^2+8$ .