Complete the table for $y = x^2 - 2x$ - OCR - GCSE Maths - Question 7 - 2017 - Paper 1
Question 7
Complete the table for $y = x^2 - 2x$.
| $x$ | -1 | 0 | 1 | 2 | 3 | 4 |
|-----|----|---|---|---|---|---|
| $y$ | 3 | 0 | -1| 0 | 3 | 8 |
Draw the graph of $y = x^... show full transcript
Worked Solution & Example Answer: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 can substitute the values of x into the equation y=x2−2x:
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
Thus, the completed table becomes:
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 from the completed table:
The point (−1,3)
The point (0,0)
The point (1,−1)
The point (2,0)
The point (3,3)
The point (4,8)
Connect these points smoothly to form a parabolic curve, ensuring that it passes through all defined points for the given range of x.
Step 3
Use your graph to solve $x^2 - 2x = 2$
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Answer
To solve the equation using the graph, rearrange it to the form y=0:
x2−2x−2=0
Now, we need to find the points at which the graph intersects the line y=2. By observing the graph drawn in part (b), the points of intersection can be identified.
From the graph, it can be determined that the solutions for x are approximately x≈2.9 and x≈−0.9. Therefore, the solutions to x2−2x=2 are:
