Chapter 8.5, Problem 34E

To determine

To match:The function with its graph.

Answer to Problem 34E

The graph that is matched with the given function isB

Explanation of Solution

Given function: $y=\left(x-5\right)\left(x-3\right)$

Given graphs:

  

Calculation:

We know that equation $y=a{\left(x-h\right)}^2+k$ represents an upward parabola with vertex at point $\left(h,k\right)$ if $a>0$ and represents a downward parabola with vertex at point $\left(h,k\right)$ if $a<0$ .

Given quadratic function can be written as

  $\begin{array}{l}y=\left(x-5\right)\left(x-3\right)\\ y=x^2-8x+15\\ y=\left(x^2-8x+16\right)-1\\ y={\left(x-4\right)}^2-1\end{array}$

Comparing it with $y=a{\left(x-h\right)}^2+k$ , we get

  $a=1,h=4,k=-1$

Therefore, given quadratic function represents an upward parabola with vertex at point (4,-1)

The x-intercepts of the curve are points where $y=0$

  $\begin{array}{l}0=\left(x-5\right)\left(x-3\right)\\ x=3,5\end{array}$

That is x-intercepts are the points (3,0) and (5,0).

The y-intercept is the point where x=0

  $y=\left(0-5\right)\left(0-3\right)=15$

That is y-intercept of the curve is (0,-15).

Therefore, graph of quadratic function is