Chapter 8, Problem 9CT

To determine

To identify: Given table is linear, quadratic or exponential

Answer to Problem 9CT

Quadratic function

  $f(x)=-2x^2$

Explanation of Solution

Given information: A table with x and y values.

Calculation:

To determine whether the table represents linear, quadratic or exponential, we need to analyze the y values

Find the difference in y values

y	-8	-2	0	-2	-8
I difference		6	2	-2	-6
II difference			-4	-4	-4

Second difference is a constant -4. So the given function is quadratic

Hence, it is a quadratic function

The values of y are same before and after 0. So vertex is (0, 0)

Vertex from of quadratic function is

  $\begin{array}{l}$ f(x)=a{(x-h)}^2+k$\text{(h,k)}\text{is}\text{the}\text{vertex}\\ $ f(x)=a{(x-0)}^2+0$f(x)=a{x}^2\end{array}$

To find the value of ‘a’ use any point from the table

(1,-2)

  $\begin{array}{l}f(x)=a{x}^2\\ (1,-2)\\ $ -2=a{(1)}^2$a=-2\\ f(x)=-2x^2\end{array}$

Therefore, given table represents a quadratic function.