7. (a) Complete the table for $y = x^2 - 2x$ - OCR - GCSE Maths - Question 7 - 2017 - Paper 1
Question 7
7.
(a) Complete the table for $y = x^2 - 2x$.
| x | -1 | 0 | 1 | 2 | 3 | 4 |
|---|----|---|---|---|---|---|
| y | 3 | 0 | -1| 0 | 3 | 8 |
(b) Draw the graph of $... show full transcript
Worked Solution & Example Answer:7. (a) Complete the table for $y = x^2 - 2x$ - OCR - GCSE Maths - Question 7 - 2017 - Paper 1
Step 1
Complete the table for $y = x^2 - 2x$
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Answer
To complete the table, we substitute each value of x into the equation to find the corresponding y values:
For x=−1: y=(−1)2−2(−1)=1+2=3
For x=0: y=(0)2−2(0)=0−0=0
For x=1: y=(1)2−2(1)=1−2=−1
For x=2: y=(2)2−2(2)=4−4=0
For x=3: y=(3)2−2(3)=9−6=3
For x=4: y=(4)2−2(4)=16−8=8
The completed table is:
x
-1
0
1
2
3
4
y
3
0
-1
0
3
8
Step 2
Draw the graph of $y = x^2 - 2x$ for $-1 \leq x \leq 4$
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Answer
To draw the graph, plot the points obtained in the table on a coordinate system with x on the horizontal axis and y on the vertical axis. The points to plot are:
(−1,3)
(0,0)
(1,−1)
(2,0)
(3,3)
(4,8)
Connect these points smoothly to form a parabolic curve. Ensure that the graph is drawn within the limits specified (−1≤x≤4).
Step 3
Use your graph to solve $x^2 - 2x = 2$
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Answer
To solve x2−2x=2, we can rearrange this to find the points where the graph intersects the line y=2:
This results in the equation y=x2−2x−2=0. From the graph, identify the x values where the curve intersects this line. The solutions can be found where the y value equals 2.
Note the approximate x values from the graph, indicating the solutions to the equation.
