Sec 4 G1 Maths Drawing quadratic graphs worksheet with answers
A free Sec 4 G1 Maths worksheet on drawing quadratic graphs: 7 questions, 31 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.
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Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.
Section A
1
The diagram shows the graph of y=−x2+4. Write down the x-coordinates of the points where the curve crosses the x-axis.
Answer[1]
2
The diagram shows the graph of y=x2+6x+6. Write down the coordinates of the minimum point of the curve.
Answer[1]
3
(a)Complete the table of values for y=x2+1.
Answer (a)[3]
(b)Complete the table of values for y=−2x2−x−4.
Answer (b)[3]
4
(a)Complete the table of values for y=x2−2x+6.
Answer (a)[3]
(b)Complete the table of values for y=6+4x−x2.
Answer (b)[3]
Section B
5
(a)The diagram shows the graph of y=x2+4x+2. Write down the coordinates of the minimum point of the curve.
Answer (a)[1]
(b)The diagram shows the graph of y=x2+3x+1. Use the graph to find the value of y when x=−1.
Answer (b)[1]
(c)Complete the table of values for y=x2−3x+6.
Answer (c)[3]
6
(a)The diagram shows the graph of y=−x2+6x−3. Use the graph to find the values of x when y=−3.
Answer (a)[1]
(b)The diagram shows the graph of y=x2+4x+2. Write down the coordinates of the minimum point of the curve.
Answer (b)[1]
(c)Complete the table of values for y=−x2−3x+1.
Answer (c)[3]
7
(a)The diagram shows the graph of y=−x2−6x−8. Write down the x-coordinates of the points where the curve crosses the x-axis.
Answer (a)[1]
(b)(i)Complete the table of values for y=x2+6.
Answer (b)(i)[3]
(b)(ii)Complete the table of values for y=2x2+x+1.
Answer (b)(ii)[3]
END OF PAPER
Answers and worked solutions
Question 1
Answer: The curve crosses the x-axis at x=−2 and x=2.[1]
The curve crosses the x-axis at x=−2 and x=2.
Question 2
Answer: The minimum point is (−3,−3).[1]
The minimum point is (−3,−3).
Question 3
(a)Answer: The y-values are the same for x=−3 and x=3, and so on: they are symmetrical about x=0.[3]
When x=−4:y=(−4)2+1=16+1=17When x=−3:y=(−3)2+1=9+1=10When x=0:y=(0)2+1=0+1=1When x=3:y=(3)2+1=9+1=10The y-values are the same for x=−3 and x=3, and so on: they are symmetrical about x=0.
(b)Answer: The line of symmetry is x=−0.25: the y-values on either side of it match.[3]
When x=−3:y=−2(−3)2−(−3)−4=−18+3−4=−19When x=0:y=−2(0)2−(0)−4=0−4=−4When x=3:y=−2(3)2−(3)−4=−18−3−4=−25The line of symmetry is x=−0.25: the y-values on either side of it match.
Question 4
(a)Answer: The y-values are the same for x=−1 and x=3, and so on: they are symmetrical about x=1.[3]
When x=−1:y=(−1)2−2(−1)+6=1+2+6=9When x=0:y=(0)2−2(0)+6=0+6=6When x=1:y=(1)2−2(1)+6=1−2+6=5When x=2:y=(2)2−2(2)+6=4−4+6=6The y-values are the same for x=−1 and x=3, and so on: they are symmetrical about x=1.
(b)Answer: The line of symmetry is x=2: the y-values on either side of it match.[3]
When x=−4:y=6+4(−4)−(−4)2=6−16−16=−26When x=−3:y=6+4(−3)−(−3)2=6−12−9=−15When x=1:y=6+4(1)−(1)2=6+4−1=9The line of symmetry is x=2: the y-values on either side of it match.
Question 5
(a)Answer: The minimum point is (−2,−2).[1]
The minimum point is (−2,−2).
(b)Answer: y=−1[1]
From x=−1, go down to the curve, then across to the y-axis.y=−1
(c)Answer: The y-values are the same for x=−1 and x=4, and so on: they are symmetrical about x=1.5.[3]
When x=−1:y=(−1)2−3(−1)+6=1+3+6=10When x=0:y=(0)2−3(0)+6=0+6=6When x=4:y=(4)2−3(4)+6=16−12+6=10When x=5:y=(5)2−3(5)+6=25−15+6=16The y-values are the same for x=−1 and x=4, and so on: they are symmetrical about x=1.5.
Question 6
(a)Answer: x=0 or x=6[1]
The line y=−3 meets the curve at two points.x=0 or x=6
(b)Answer: The minimum point is (−2,−2).[1]
The minimum point is (−2,−2).
(c)Answer: The y-values are the same for x=−3 and x=0, and so on: they are symmetrical about x=−1.5.[3]
When x=−2:y=−(−2)2−3(−2)+1=−4+6+1=3When x=−1:y=−(−1)2−3(−1)+1=−1+3+1=3When x=3:y=−(3)2−3(3)+1=−9−9+1=−17The y-values are the same for x=−3 and x=0, and so on: they are symmetrical about x=−1.5.
Question 7
(a)Answer: The curve crosses the x-axis at x=−4 and x=−2.[1]
The curve crosses the x-axis at x=−4 and x=−2.
(b)(i)Answer: The y-values are the same for x=−3 and x=3, and so on: they are symmetrical about x=0.[3]
When x=−2:y=(−2)2+6=4+6=10When x=0:y=(0)2+6=0+6=6When x=3:y=(3)2+6=9+6=15The y-values are the same for x=−3 and x=3, and so on: they are symmetrical about x=0.
(b)(ii)Answer: The line of symmetry is x=−0.25: the y-values on either side of it match.[3]
When x=−2:y=2(−2)2+(−2)+1=8−2+1=7When x=1:y=2(1)2+(1)+1=2+1+1=4When x=2:y=2(2)2+(2)+1=8+2+1=11The line of symmetry is x=−0.25: the y-values on either side of it match.