6. (a) Complete the table of values for $y = x^2 - 3x + 1$ - Edexcel - GCSE Maths - Question 6 - 2022 - Paper 1
Question 6
6.
(a) Complete the table of values for $y = x^2 - 3x + 1$.
| x | -1 | 0 | 1 | 2 | 3 | 4 |
|-----|------|-----|-----|-----|-----|-----|
| y | 5 |... show full transcript
Worked Solution & Example Answer:6. (a) Complete the table of values for $y = x^2 - 3x + 1$ - Edexcel - GCSE Maths - Question 6 - 2022 - Paper 1
Step 1
Complete the table of values for $y = x^2 - 3x + 1$
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Answer
To complete the table, we substitute the given values of x into the equation.
For x=−1: y=(−1)2−3(−1)+1=1+3+1=5
Therefore, y=5.
For x=0: y=(0)2−3(0)+1=0−0+1=1
Therefore, y=1.
For x=1: y=(1)2−3(1)+1=1−3+1=−1
Therefore, y=−1.
For x=2: y=(2)2−3(2)+1=4−6+1=−1
Therefore, y=−1.
For x=3: y=(3)2−3(3)+1=9−9+1=1
Therefore, y=1.
For x=4: y=(4)2−3(4)+1=16−12+1=5
Therefore, y=5.
The completed table of values is:
x
-1
0
1
2
3
4
y
5
1
-1
-1
1
5
Step 2
On the grid, draw the graph of $y = x^2 - 3x + 1$
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Answer
After plotting the points from the completed table on the grid, connect these points smoothly to form a parabola. The key points to plot are:
(−1,5)
(0,1)
(1,−1)
(2,−1)
(3,1)
(4,5)
Ensure to label the axes correctly and to draw a continuous curve through the points.
Step 3
Using your graph, find estimates for the solutions of the equation $x^2 - 3x + 1 = 0$
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Answer
To find the estimates of the solutions, look for the x-intercepts of the graph where the curve intersects the x-axis. The estimates can be observed to be approximately:
xextaround0.3 and xextaround2.7.
These points suggest that there are two solutions to the equation x2−3x+1=0.
