Linear and quadratic models
Answers are for parents and teachers.
1
A bamboo shoot’s height is L(t) = 25 + 4t cm (t in days). How tall is it after 10 days, in cm?
65
2
Find the vertex of y = x² − 10x + 7.
(5, −18)
3
A ball thrown upward from a 15 m balcony has height H(t) = −5t² + 10t + 15 (m). Find its greatest height and when it lands.
The vertex is at t = 1 s, H(1) = 20 m; −5(t² − 2t − 3) = 0 ⇒ t = 3 s (t = −1 is rejected).
4
A parabola meets the x-axis at x = 1 and x = 7 and passes through (2, −10). Write its formula.
y = a(x − 1)(x − 7); a · 1 · (−5) = −10 ⇒ a = 2; y = 2x² − 16x + 14
5
Why must a ≠ 0 in y = ax² + bx + c?
If a = 0, the x² term vanishes and the function becomes linear, y = bx + c, whose graph is a line, not a parabola.