## Algebra 1

Published by Prentice Hall

# Chapter 4 - An Introduction to Functions - 4-1 Using Graphs to Relate Two Quantities - Practice and Problem-Solving Exercises - Page 244: 16

#### Answer

The function for this relation is y=0.5$x^{2}$. The graph of this is shown in the screenshot below.

#### Work Step by Step

The function for the relation (0, 0), (1, 0.5), (2, 2), (3, 4.5), (4, 8) was created by taking the first difference of the y values and then the second difference of the first difference. if the second difference is equal across the x values, then the function is quadratic. So to find the equation of the function we know since it is quadratic we can write y=a$x^{2}$. To find a we can plug in one of the values (1,0.5), 0.5 = a($1)^{2}$ a= 0.5 (2,2) 2 = a($2)^{2}$ 2=4a a=$\frac{2}{4}$ = 0.5 Therefore y=0.5$x^{2}$

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