Examples of Quadratic Functions

Maximum height

Height $h(t) = -5t^2 + 20t + 1$ (m, seconds). Maximum height?

1. Vertex time: $t = 20/(2 \cdot 5) = 2$.
2. $h(2) = -20 + 40 + 1 = 21$.

Жауап: 21 m at $t = 2$ s

Fenced rectangle

A farmer has 40 m of fencing for three sides of a rectangular pen against a wall. Maximum area?

1. Sides: width $w$, length $40 - 2w$.
2. Area $A(w) = w(40 - 2w) = 40w - 2w^2$.
3. Vertex: $w = 40/4 = 10$, length $20$.
4. Max area: $200$ m².

Жауап: 200 m² when $w = 10$, $\ell = 20$