Chapter 4.6, Problem 52S

To determine

Find the type of function using given graph.

Answer to Problem 52S

The graph represents the quadratic function.

Explanation of Solution

Given:

The given graph is

  

Calculation:

The given graph is the form of parabola. Parabola represents the graph of a quadratic function.

Use standard form of the quadratic function $f\left(x\right)=a{\left(x-h\right)}^2+k$ , where $\left(h,k\right)$ is the vertex of the parabola.

In the given graph,

Vertex is $\left(1,-2\right)$ .

  $\left(x,y\right)$ is any point on the graph.

Take any point $\left(x,y\right)$ from the given graph.

  $\left(x,y\right)=\left(0,0\right)$

Substitute the values of $x,y,h$ and $k$ in the standard function.

  $\begin{array}{l}0=a{\left(0-1\right)}^2+\left(-2\right)\\ \Rightarrow 0=a-2\\ \Rightarrow a=2\end{array}$

Hence the equation of the given parabola is $f\left(x\right)=2{\left(x-1\right)}^2-2$ .