Solutions — Parabolas 7E Worksheet
Year 10 Mathematics Core · Cambridge Ch 7, §7E · Mr Wong
ANSWER KEY
Warm-up
Q1. Discriminant and number of $x$-intercepts:
a $\Delta=16$ → two
b $\Delta=0$ → one
c $\Delta=-15$ → none
d $\Delta=17$ → two
Q2. $x$-intercepts (exact):
a $x=1\pm\sqrt6$
b $x=-2\pm\sqrt2$
Part A — Turning point
Q3. Using $x=-\tfrac{b}{2a}$:
a $(3,2)$ ($x=3$, $y=9-18+11$)
b $(-1,-5)$ ($x=-1$, $y=2-4-3$)
Part B — Sketching
Q4. $y=x^2-2x-3$:
a $y$-int $(0,-3)$
b $x$-int $(-1,0)$ and $(3,0)$
c TP $(1,-4)$ minimum
Q5. $y=2x^2+4x-3$:
a $y$-int $(0,-3)$
b $x$-int $(0.58,0)$ and $(-2.58,0)$
c TP $(-1,-5)$ minimum
Part C — Irrational intercepts
Q6. $x$-intercepts to 2 d.p.:
a $x=0.27,\ 3.73$
b none ($\Delta=-11$)
c $x=0.18,\ 2.82$
d $x=0.18,\ 1.82$
Challenge
Q7. One $x$-intercept means $\Delta=0$: $k^2-4(1)(9)=k^2-36=0$.