Chapter 9.1, Problem 4STP

For Exercises 1-4, choose the correct letter.

What is the order, form narrowest to widest graph, of the quadratic functions $f(x)=-10x^2,f(x)=2x^2,$ and $f(x)=0.5x^2?$

F. $f(x)=10x^2,f(x)2x^2,$ and $f(x)=0.5x^2$

G. $f(x)=10x^2,$

$f(x)-10x^2,$ and $f(x)=0.5x^2$

H. $f(x)=0.5x^2,f(x)=2x^2,$ and $f(x)=10x^2$

I. $f(x)=0.5x^2,f(x)=-10x^2,$ and $f(x)=2x^2$

To determine

To correct the order of graph from narrow to wide .

Answer to Problem 4STP

The correct order is option (H) $f\left(x\right)=0.5x^2;f\left(x\right)=2x^2;f\left(x\right)=-10x^2$ .

Explanation of Solution

Given information:

The general form of a parabola is $y=a{x}^2+bx+c$ .

Graph:

  

For a parabola $y=a{x}^2+bx+c$ the smaller the value of $\left|a\right|$ , the wider the graph of the parabola.

So, we arrange: $\left|10\right|,\left|2\right|,\left|0.5\right|\to 10,2,0.5$

From narrowest to widest $0.5,2,10$ .

Therefore, the correct graph is option (H) $f\left(x\right)=0.5x^2;f\left(x\right)=2x^2;f\left(x\right)=-10x^2$ .