Sketching the Parabola y = ax² + q (Grade 10) — Worksheet & Memo

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Grade 10 · Functions and Graphs

Sketching the Parabola y = ax² + q (Grade 10)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 22

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
Write down the shape and the turning point of y = 3x² − 5.
(2)
a = 3 > 0, so it opens UP ✓; turning point (0 ; −5) ✓(2)
2
Write down the y-intercept and the range of y = x² + 2.
(2)
(0 ; 2) ✓; y ≥ 2 ✓(2)
3
Determine the x-intercepts of y = x² − 9.
(2)
x² = 9 ✓, so x = −3 or x = 3 ✓(2)
4
Determine the x-intercepts of y = 2x² − 8.
(3)
2x² = 8 ✓; x² = 4 ✓; x = ±2 ✓(3)
5
Does y = x² + 5 cut the x-axis? Give a reason.
(2)
No ✓ — x² = −5 has no real solution ✓(2)
6
Write down the range of y = −x² + 4.
(2)
a < 0, so (0 ; 4) is a maximum ✓; y ≤ 4 ✓(2)
7
y = ax² + q has turning point (0 ; 1) and passes through (2 ; 9). Determine a and q.
(3)
q = 1 ✓; 9 = 4a + 1 ✓; a = 2 ✓(3)
8
Describe how y = x² − 3 differs from y = x².
(2)
The same shape ✓, moved 3 units down ✓(2)
9
Describe how y = −x² differs from y = x².
(2)
It is reflected in the x-axis ✓, so it opens downwards ✓(2)
10
Write down the domain and the range of y = 2x² − 6.
(2)
Domain x ∈ ℝ ✓; range y ≥ −6 ✓(2)

TOTAL: 22 marks