Sketching using Transformations (Ex 7B)
Year 10 Mathematics Core · Cambridge Ch 7, §7B · Mr Wong
Learning intentions.
- Name and describe the three transformations: dilation, reflection, translation
- Read the turning point straight from turning point form $y=a(x-h)^2+k$
- Sketch a parabola from turning point form, labelling the turning point and $y$-intercept
- Find the rule of a simple parabola given the turning point and one other point
Key results
For $y=a(x-h)^2+k$: turning point $(h,k)$, axis of symmetry $x=h$.
$a>0$ → upright (minimum); $a<0$ → inverted (maximum). Find the $y$-intercept by substituting $x=0$.
Part A — Reading the turning point
1. Write the coordinates of the turning point of each.
a $y=x^2+3$
b $y=-x^2-4$
c $y=(x-2)^2$
d $y=(x+5)^2$
2. For each rule state: turning point, max or min, axis of symmetry, $y$-intercept.
a $y=(x-1)^2+2$
b $y=(x+4)^2-1$
c $y=-(x-2)^2+5$
d $y=-(x+3)^2$
3. Choose the word —
left, right, up or
down — to complete each translation of $y=x^2$.
a $y=x^2+3$ is translated
b $y=(x-3)^2$ is translated
c $y=(x+1)^2$ is translated
d $y=x^2-6$ is translated
Part B — Reading a sketch
4. The parabola below has rule $y=(x-2)^2-3$. Use the graph to state each key feature.
a Max or min?
b Turning point
c Axis of symmetry
d $y$-intercept
Parabolas 7B — continued
Part C (sketching) · Part D (finding the rule) · Challenge
Part C — Sketching from turning point form
5. Sketch each parabola on the grids below. Mark the turning point, the axis of symmetry and the $y$-intercept.
Part D — Finding the rule
6. Each parabola has its turning point on the $y$-axis, so its rule is $y=ax^2+k$. Find each rule.
a TP $(0,2)$, through $(1,5)$
b TP $(0,-3)$, through $(2,5)$
Challenge
7. The parabola $y=a(x-h)^2+k$ has a
maximum turning point at $(2,5)$ and passes through the point $(0,1)$.
a State $h$ and $k$.
b Use $(0,1)$ to find $a$.