Worked example 24: Interpreting graphs
QUESTION
The graphs ofy= x^2 + 4andy=x 2 are given. Calculate the following:
1.coordinates ofA,B,C,D
2.coordinates ofE
3.distanceCDA^0 BCDEy= x^2 +4
y=x 2xySOLUTION
Step 1: Calculate the intercepts
For the parabola, to calculate they-intercept, letx= 0:
y= x^2 + 4
= 02 + 4
= 4This gives the pointC(0; 4).
To calculate thex-intercept, lety= 0:
y= x^2 + 4
0 = x^2 + 4
x^2 4 = 0
(x+ 2)(x 2) = 0
)x=± 2This gives the pointsA( 2; 0)andB(2; 0).
For the straight line, to calculate they-intercept, letx= 0:
y=x 2
= 0 2
= 2This gives the pointD(0; 2).
210 6.7. Interpretation of graphs