4. (a) Complete the table of values for $y = x^2 - 2x + 2$ - Edexcel - GCSE Maths - Question 4 - 2021 - Paper 2
Question 4
4. (a) Complete the table of values for $y = x^2 - 2x + 2$.
| x | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|-----|----|----|----|----|----|----|----|
| y | 10 | 5 | ... show full transcript
Worked Solution & Example Answer:4. (a) Complete the table of values for $y = x^2 - 2x + 2$ - Edexcel - GCSE Maths - Question 4 - 2021 - Paper 2
Complete the table of values for $y = x^2 - 2x + 2$
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To complete the table, substitute the given values of x into the equation to calculate y.
- For x=−2:
y=(−2)2−2(−2)+2=4+4+2=10
- For x=−1:
y=(−1)2−2(−1)+2=1+2+2=5
- For x=0:
y=(0)2−2(0)+2=0−0+2=2
- For x=1:
y=(1)2−2(1)+2=1−2+2=1
- For x=2:
y=(2)2−2(2)+2=4−4+2=2
- For x=3:
y=(3)2−2(3)+2=9−6+2=5
- For x=4:
y=(4)2−2(4)+2=16−8+2=10
The completed table is shown above.
On the grid, draw the graph of $y = x^2 - 2x + 2$ for values of $x$ from -2 to 4.
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To draw the graph, plot the points from the completed table.
- Mark the points:
- (-2, 10)
- (-1, 5)
- (0, 2)
- (1, 1)
- (2, 2)
- (3, 5)
- (4, 10)
Connect these points smoothly to form a parabolic curve.
Use your graph to find estimates of the solutions of the equation $x^2 - 2x + 2 = 4$.
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To estimate the solutions, set y=4 and look for the intersection points of the graph y=x2−2x+2 with the horizontal line y=4.
- By examining the graph, you can observe that the solutions appear to be approximately xhickapprox−0.5 and xhickapprox2.5.
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