# Question Video: Completing a Table of Values for a Quadratic Function Mathematics

Complete the following table for the graph of π(π₯) = 2π₯Β² by finding the unknowns π and π.

02:18

### Video Transcript

Complete the following table for the graph of π of π₯ equals two π₯ squared by finding the unknowns π and π.

Weβve been given the function π of π₯ equals two π₯ squared and asked to complete a table of values that could then be used to plot the graph of π of π₯. The completed table will contain ordered pairs of π₯, π of π₯ values that will give the coordinates of points that lie on the graph of π of π₯. For example, weβre given that when π₯ is equal to negative two, π of π₯ is equal to eight. So the point with coordinates negative two, eight lies on the graph of π of π₯, as do the points with coordinates zero, zero and one, two.

We are asked to find the unknowns π and π, which, we can see, are the π of π₯ values associated with π₯-values of negative one and positive two. In other words, π of negative one is equal to π, and π of two is equal to π. We can therefore find the values of π and π by substituting π₯ equals one and then π₯ equals two into the function π of π₯.

To find π first of all then, we substitute π₯ equals negative one. π of negative one is two multiplied by negative one squared. Thatβs two multiplied by one, which is equal to two. And so we find that π is equal to two. To find π, we substitute π₯ equals two into the function π of π₯. π of two is equal to two multiplied by two squared. Thatβs two multiplied by four, which is equal to eight. And so weβve also found the value of π.

We now know that the points with coordinates negative one, two and two, eight also lie on the graph of π of π₯. If we wanted, we could plot these five coordinates on a coordinate grid and then join the points together with a curve to give the graph of π of π₯.

Weβve answered the question, though, which was to determine the values of the unknowns π and π. π is equal to two, and π is equal to eight.