Solutions — Parabolas 7F Worksheet
Year 10 Mathematics Core · Cambridge Ch 7, §7F · Mr Wong
ANSWER KEY
Part A — Reading a graph
Q1. $h=-(t-3)^2+9$:
a $t=3$ s
b $9$ m
c $t=6$ s ($(t-3)^2=9$)
Q2. $h=30t-5t^2$:
a $45$ m (at $t=3$)
b $t=6$ s
c $0\le t\le 6$
Part B — A bridge cable
Q3. $h=(d-3)^2+2$, $0\le d\le6$:
a $2$ m
b at $d=3$
c $11$ m at each pillar ($d=0$ and $d=6$)
Part C — Forming a model
Q4. 24 m fence, width $x$:
a $L=12-x$
b $A=x(12-x)=12x-x^2$
c $0
d max $36$ m² at $6\times6$
Part D — A rocket
Q5. $h=40t-5t^2$:
a $t=4$ s
b $80$ m
c $t=8$ s
d $0\le t\le 8$
Q6. Garden bed, 16 m for 3 sides:
a $L=16-2x$
b $A=x(16-2x)$
c max $32$ m² (at $x=4$)
d $4\text{ m}\times8\text{ m}$
Challenge — river enclosure
Q7. 60 m for three sides ($2x+L=60$):
a $L=60-2x$
b $A=x(60-2x)=60x-2x^2$
c $A=-2(x-15)^2+450$
d max $450$ m² at $x=15$, $L=30$ ($15\text{ m}\times30\text{ m}$)