Chapter 8.5, Problem 59E

To determine

To find: the quadratic function represented by the graph.

Answer to Problem 59E

  $y=-4x^2+8x+32$

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(−2,0), B(4,0), C(2,32), find the quadratic function using system of equations method,

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

Substitute A(−2,0), in the quadratic function,

  $\begin{array}{l}a{\left(-2\right)}^2+b\left(-2\right)+c=0\\ 4a-2b+c=0\mathrm{...}(1)\end{array}$

Substitute B(4, 0), in the quadratic function,

  $\begin{array}{l}a{\left(4\right)}^2+b\left(4\right)+c=0\\ 16a+4b+c=0\mathrm{...}(2)\end{array}$

Substitute C(2, 32) in the quadratic function,

  $\begin{array}{l}a{\left(2\right)}^2+b\left(2\right)+c=32\\ 4a+2b+c=32\mathrm{...}(3)\end{array}$

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

From the equation (1), (2) and (3),

We get,

  $a=-4$ , $b=8$ and $c=32$ ,

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

  $y=-4x^2+8x+32$

This is the required quadratic function.