Chapter 8.5, Problem 58E

To determine

To find: the quadratic function represented by the given graph.

Answer to Problem 58E

  $y=-x^2+8x-7$

Explanation of Solution

Given information: graph

  

To find the quadratic function for given graph, use with 3 points on the curve to form 3 equation, and solve them to get required result,

Here 3 points are given,

Consider A(1,0), B(7,0), C(6,5), find the quadratic function using system of equations method,

The general form of quadratic function, $y=a{x}^2+bx+c$ .

Substitute A(1,0), in the quadratic function,

  $\begin{array}{l}a{\left(1\right)}^2+b\left(1\right)+c=0\\ a+b+c=0\mathrm{...}(1)\end{array}$

Substitute B(7,0), in the quadratic function,

  $\begin{array}{l}a{\left(7\right)}^2+b\left(7\right)+c=0\\ 49a+7b+c=0\mathrm{...}(2)\end{array}$

Substitute C(6,5) in the quadratic function,

  $\begin{array}{l}a{\left(6\right)}^2+b\left(6\right)+c=5\\ 36a+6b+c=-8\mathrm{...}(3)\end{array}$

Therefore from all the three equation solve the value of a, b, c.

From the equation (1) and (2), and substitute this in first and then from first and third equation,

We get,

  $a=-1$ , $b=8$ and ,

The value of a, b and c substitute in standard equation of quadratic equation,

  $y=-x^2+8x-7$

This is the required quadratic function.