Exploring Parabolas (Ex 7A)
Year 10 Mathematics Core · Cambridge Ch 7, §7A · Mr Wong
Learning intentions.
- Know the shape, vertex and symmetry of the basic parabola $y=x^2$
- Read key features from a graph: turning point (max/min), axis of symmetry, $x$- and $y$-intercepts
- Describe transformations of $y=x^2$: dilation (wider/narrower), reflection ($a<0$), translation
Key results
$y=x^2$ has vertex $(0,0)$ (a minimum), axis of symmetry $x=0$.
In $y=ax^2$: larger $|a|$ → narrower, smaller $|a|$ → wider, and $a<0$ → reflected (opens down).
Warm-up — the basic parabola
1. Complete the table of values for $y=x^2$.
| $x$ | $-3$ | $-2$ | $-1$ | $0$ | $1$ | $2$ | $3$ |
|---|
| $y=x^2$ | | | | | | | |
2. Using your table from Q1, state for $y=x^2$:
a turning point
b max or min?
c axis of symmetry
d $y$-intercept
Part A — Reading key features from a graph
3. For the parabola graphed below, state each key feature.
a Max or min?
b Turning point
c Axis of symmetry
d $x$-intercepts
e $y$-intercept
4. A parabola has a
maximum turning point at $(-2,4)$ and crosses the $x$-axis at $-5$ and $1$.
a axis of symmetry
b $x$-intercepts