a < 0 a > 0q > 0q= 0q < 0Table 6.2:The effect ofaandqon a parabola.VISIT:
You can use thisPhet simulationto help you see the effects of changingaandqfor a parabola.Discovering the characteristics EMA4M
The standard form of the equation of a parabola isy=ax^2 +q.
Domain and range
The domain isfx:x 2 Rgbecause there is no value for whichf(x)is undefined.
Ifa > 0 then we have:
x^2 0 (Perfect square is always positive)
ax^2 0 (sincea >0)
ax^2 +q q (addqto both sides)
)f(x) q
Therefore ifa > 0 , the range is[q; 1 ). Similarly, ifa < 0 then the range is( 1;q].
Worked example 5: Domain and range of a parabolaQUESTION
Ifg(x) =x^2 + 2, determine the domain and range of the function.Chapter 6. Functions 161