Complete the table of values for $y = x^2 - 2x + 2$ - Edexcel - GCSE Maths - Question 5 - 2021 - Paper 2
Question 5
Complete the table of values for $y = x^2 - 2x + 2$.
| $x$ | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|-----|----|----|---|---|---|---|---|
| $y$ | 10 | 5 | 2 | 1 | 2 | 5 | 1... show full transcript
Worked Solution & Example Answer:Complete the table of values for $y = x^2 - 2x + 2$ - Edexcel - GCSE Maths - Question 5 - 2021 - Paper 2
Step 1
Complete the table of values for $y = x^2 - 2x + 2$
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Answer
To complete the table, calculate the value of y for each x by substituting into the equation:
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:
x
-2
-1
0
1
2
3
4
y
10
5
2
1
2
5
10
Step 2
On the grid, draw the graph of $y = x^2 - 2x + 2$ for values of $x$ from -2 to 4
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Answer
To draw the graph, plot the points calculated in the previous step on the grid. Connect these points with a smooth, continuous curve to represent the quadratic function.
Step 3
Use your graph to find estimates of the solutions of the equation $x^2 - 2x + 2 = 4$
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Answer
To find the solutions of the equation x2−2x+2=4, rearrange to x2−2x−2=0. Plot the horizontal line y=4 on the graph and observe where it intersects the curve. The estimated x values for these points of intersection are approximately xextvaluesbetween0.5extand1.5.
