Everything Maths Grade 10

9.James and Themba both throw a stone from the top of a building into a river. The path travelled by the

stones can be described by quadratic equations.y= 201 x^2 + 5describes the path of the stone thrown

by James andy= 451 x^2 + 5describes the path of Themba’s stone.

y= 201 x^2 +5

y= 451 x^2 +5

A

B C

x

y

a)What is the height of the building that they stood on?

b)How far did James throw his stone before it hit the river surface?

c)How much farther did Themba throw his stone before it hit the river surface?

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1a.2FWD 1b.2FWF 1c.2FWG 1d.2FWH 1e.2FWJ 1f.2FWK 2a.2FWM

2b.2FWN 2c.2FWP 2d.2FWQ 3a.2FWR 3b.2FWS 3c.2FWT 4a.2FWV

4b.2FWW 5a.2FWX 5b.2FWY 6.2FWZ 7.2FX2 8.2FX3 9.2FX4

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6.2 Linear functions EMA48

Functions of the formy=x EMA49

Functions of the formy=mx+care called straight line functions. In the equation,y=mx+c,mandcare
constants and have different effects on the graph of the function.

Worked example 1: Plotting a straight line graph

QUESTION

y=f(x) =x

Complete the following table forf(x) =xand plot the points on a set of axes.

x  2  1 0 1 2

f(x)  2

1.Join the points with a straight line.

2.Determine the domain and range.

3.About which line isfsymmetrical?

4.Using the graph, determine the value ofxfor whichf(x) = 4. Confirm your answer graphically.

5.Where does the graph cut the axes?

150 6.2. Linear functions