Everything Maths Grade 10

SOLUTION

Step 1: Examine the sketch

From the sketch we see that the graph is a sine graph that has been shifted vertically upwards. The general
form of the equation isy=asin+q.

Step 2: Substitute the given points into equation and solve

AtN,= 210°andy= 0:

y=asin+q

0 =asin 210 °+q

=a

(

1

2

)

+q

)q=

a

2

AtM,= 90°andy=^32 :

3

2

=asin 90 °+q

=a+q

Step 3: Solve the equations simultaneously using substitution

3

2

=a+q

=a+

a

2

3 = 2a+a

3 a= 3

)a= 1

)q=

a

2

=

1

2

Step 4: Write the final answer

y=sin+^12

Exercise 6 – 7:

1.Plot the following functions on the same set of axes and clearly label all the points at which the functions

intersect.

a) y=x^2 + 1andy= 3x b)y=xandy=

2

x

c) y=x^2 + 3andy= 6 d)y=x^2 andy=

8

x

212 6.7. Interpretation of graphs