Sketching the Parabola: The Complete Exam Guide — Worksheet & Memo

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Grade 10 · Functions

Sketching the Parabola: The Complete Exam Guide

EXAM-STYLE CLASS TEST

Marks

Duration

55 minutes

Questions

Name:

Class:

Date:

Mark

/ 35

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
The axis of symmetry of y = x² − 4x + 3 is …
(1)
A)x = 2
B)x = −2
C)x = 4
D)x = 3
1.2
The turning point of y = x² − 4x + 3 is …
(1)
A)(2 ; −1)
B)(2 ; 3)
C)(−2 ; 15)
D)(2 ; 1)
1.3
The x-intercepts of y = x² − 4x + 3 are …
(1)
A)x = 1 and x = 3
B)x = −1 and x = −3
C)x = 3 only
D)x = 4 and x = 3
1.4
The graph of y = −2x² + 5 …
(1)
A)has a maximum turning point
B)has a minimum turning point
C)is a straight line
D)has no turning point
1.5
The range of y = x² + 2 is …
(1)
A)y ≥ 2
B)y ≤ 2
C)y ≥ 0
D)y ∈ R
1.6
For y = a(x − p)² + q, the turning point is …
(1)
A)(p ; q)
B)(−p ; q)
C)(p ; −q)
D)(q ; p)
1.7
If the discriminant of a quadratic is NEGATIVE, its parabola …
(1)
A)does not cut the x-axis
B)touches the x-axis once
C)cuts the x-axis twice
D)is a straight line
1.8
y = x² − 6x + 8 written in turning-point form is …
(1)
A)y = (x − 3)² − 1
B)y = (x − 3)² + 8
C)y = (x − 6)² − 28
D)y = (x + 3)² − 1
1.9
A parabola cuts the x-axis at 2 and at 6 and passes through (0 ; 12). Its equation is …
(1)
A)y = (x − 2)(x − 6)
B)y = (x + 2)(x + 6)
C)y = 12(x − 2)(x − 6)
D)y = (x − 2)(x − 6) + 12
1.10
A parabola has x-intercepts −1 and 5. Its axis of symmetry is …
(1)
A)x = 2
B)x = 4
C)x = 3
D)x = −3

Answer grid — circle your answers for Question 1

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[13 MARKS]

Given f(x) = x² − 4x + 3.

2.1
Write down the shape of the graph and give a reason.
(2)
2.2
Calculate the coordinates of the x-intercepts and the y-intercept.
(5)
2.3
Calculate the coordinates of the turning point.
(4)
2.4
Write down the range of f.
(2)

Question 3

[12 MARKS]

Answer the questions below about parabolas.

3.1
Determine, using the discriminant, whether y = x² + x + 4 cuts the x-axis.
(4)
3.2
For y = −2x² + 8x − 6, determine the coordinates of the turning point.
(4)
3.3
Explain what happens to the graph of y = x² when q is changed in y = x² + q, and what happens when a is made negative.
(4)

TOTAL: 35 marks

This question paper consists of 3 questions.

Statement	Reason