A rocket is launched into the air. Its height h above the ground is given by h = 8x − 2x 2 , where h is its height in hundreds of metres and x is its distance horizontally from the launch site in hundreds of metres. Plot h against x in the domain 0 ≤ x ≤ 4, x ∈ .
Solution h = 8(x) − 2(x) 2
x h
0 1234 0 6860
h
5 6 7 8
3 4
1 2
0 1 2 34 x Hundreds of metres
General shape of quadratic functions The general shape of all quadratic functions, y = a x 2 + bx + c, is either:
Opens up
a > 0 Cup If a > 0, the curve opens up
y = 4 x 2 − x has a ∪ shape. If a < 0, the curve opens down
like a cup. Cap like a cap.
y = − x 2 + 5x − 57 has a ∩ shape. You will see why quadratic functions have this shape in Section 8: Differentiation.
