Everything Maths Grade 10

6.3 Quadratic functions EMA4H

Functions of the formy=x^2 EMA4J

Functions of the general formy=ax^2 +qare called parabolic functions. In the equationy=ax^2 +q,aand
qare constants and have different effects on the parabola.

Worked example 4: Plotting a quadratic function

QUESTION

y=f(x) =x^2

Complete the following table forf(x) =x^2 and plot the points on a system of axes.

x  3  2  1 0 1 2 3

f(x) 9

1.Join the points with a smooth curve.

2.The domain offisx 2 R. Determine the range.

3.About which line isfsymmetrical?

4.Determine the value ofxfor whichf(x) = 6^14. Confirm your answer graphically.

5.Where does the graph cut the axes?

SOLUTION

Step 1: Substitute values into the equation

f(x) =x^2

f(3) = (3)^2 = 9

f(2) = (2)^2 = 4

f(1) = (1)^2 = 1

f(0) = (0)^2 = 0

f(1) = (1)^2 = 1

f(2) = (2)^2 = 4

f(3) = (3)^2 = 9

x  3  2  1 0 1 2 3

f(x) 9 4 1 0 0 4 9

Step 2: Plot the points and join with a smooth curve

From the table, we get the following points:(3; 9);(2; 4);(1; 1);(0; 0);(1; 1);(2; 4);(3; 9)

158 6.3. Quadratic functions