Chapter 2.1, Problem 5E

To determine

To match:The quadratic function with its graph.

Answer to Problem 5E

The graph (c) is the graph of quadratic function $f\left(x\right)={\left(x-2\right)}^2$ .

Explanation of Solution

Given data: $y$

The given quadratic function is $f\left(x\right)={\left(x-2\right)}^2$ . The graphs are shown in figure here.

  

Method/Formula used:

The standard form of quadratic function $f\left(x\right)=a{\left(x-h\right)}^2+k$ represents a parabola with the vertex is $\left(h,k\right)$ . If $a>0$ then the parabola has minima at the vertex, so concave upwards, and if $a<0$ then the parabola has maxima at the vertex so concave downwards.

Calculation:

The given quadratic function is $f\left(x\right)={\left(x-2\right)}^2$ may be written as

  $f\left(x\right)=1.{\left(x-2\right)}^2+0$................. (1)

Now, comparing equation (1) with the function $f\left(x\right)=a{\left(x-h\right)}^2+k$ , we have $a=1$ , $h=2$ , and $k=0$ .

Since, $a=1>0$ hence the parabola is has minimum at the vertex so is concave upwards, and $\left(2,0\right)$ is the vertex of the parabola

Thus, the quadratic function $f\left(x\right)={\left(x-2\right)}^2$ is the equation of a parabola that is concave upwards with vertex $\left(2,0\right)$ that matches with the graph (c).

Hence, the graph (c) is the graph of quadratic function $f\left(x\right)={\left(x-2\right)}^2$

Conclusion:

The graph (c) is the graph of quadratic function $f\left(x\right)={\left(x-2\right)}^2$ .