4. (a) 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 | 10 |
(b) On the grid, draw the graph of $y = x^2 - 2x + 2$ for values of $x$ from -2 to 4 - Edexcel - GCSE Maths - Question 5 - 2021 - Paper 2
Question 5
4. (a) 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 |... show full transcript
Worked Solution & Example Answer:4. (a) 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 | 10 |
(b) On the grid, draw the graph of $y = x^2 - 2x + 2$ for values of $x$ from -2 to 4 - 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 of values, we substitute each value of x into the equation y=x2−2x+2:
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
Thus, the completed table of values 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
Plot the points from the completed table onto the grid. The points are:
(−2,10)
(−1,5)
(0,2)
(1,1)
(2,2)
(3,5)
(4,10)
Connect these points with a smooth 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, we rewrite it as x2−2x−2=0.
On the graph, locate the points where the curve of y=x2−2x+2 intersects the line y=4. From the graph:
The estimates of the x-values where the intersections occur appear to be approximately xoughly1.5 and xoughly3.5. These values are estimates based on visual interpretation of the graph.
