Solutions — Y10 Core Parabolas 7A Worksheet

Warm-up

Q1. Table of values for $y=x^2$:

$x$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$
$y=x^2$	9	4	1	0	1	4	9

Q2. Features of $y=x^2$:

a $(0,0)$

b minimum

c $x=0$

d $(0,0)$

Q3. The graphed parabola $y=x^2-2x-3$:

a minimum

b $(1,-4)$

c $x=1$

d $(-1,0)$ and $(3,0)$

e $(0,-3)$

Q4. Maximum at $(-2,4)$, crosses $x$-axis at $-5$ and $1$:

a $x=-2$

b $(-5,0)$ and $(1,0)$

Q5. max/min · reflected? · turning point · vs $y=x^2$:

a $y=3x^2$: min · no · $(0,0)$ · narrower

b $y=-2x^2$: max · yes · $(0,0)$ · narrower

c $y=\tfrac14 x^2$: min · no · $(0,0)$ · wider

d $y=(x-3)^2$: min · no · $(3,0)$ · same

e $y=x^2+2$: min · no · $(0,2)$ · same

f $y=-x^2+4$: max · yes · $(0,4)$ · same

Q6. Tables ($y=2x^2$ is narrower; $y=\tfrac12 x^2$ is wider):

$x$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$
$y=2x^2$	18	8	2	0	2	8	18
$y=\tfrac12 x^2$	4.5	2	0.5	0	0.5	2	4.5

Q7. Table for $y=x^2-4$:

$x$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$
$y=x^2-4$	5	0	-3	-4	-3	0	5

a turning point $(0,-4)$

b $x$-intercepts $(-2,0)$ and $(2,0)$

Q8. Table for $y=(x-3)(x+1)$:

$x$	$-2$	$-1$	$0$	$1$	$2$	$3$	$4$
$y$	5	0	-3	-4	-3	0	5

· $x$-intercepts at $(-1,0)$ and $(3,0)$; halfway is $x=1$, giving turning point $(1,-4)$ (a minimum).