Complete the table for $y = x^2 - 4x + 1$ - OCR - GCSE Maths - Question 7 - 2019 - Paper 1
Question 7
Complete the table for $y = x^2 - 4x + 1$.
| x | -1 | 0 | 1 | 2 | 3 | 4 | 5 |
|-----|----|----|----|----|----|----|----|
| y | 6 | 1 | -2 | 1 | 6 | 13... show full transcript
Worked Solution & Example Answer:Complete the table for $y = x^2 - 4x + 1$ - OCR - GCSE Maths - Question 7 - 2019 - Paper 1
Step 1
Complete the table for $y = x^2 - 4x + 1$
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Answer
To complete the table, we need to calculate the values of y for each corresponding value of x given in the table. We apply the formula:
For x=−1:
y=(−1)2−4(−1)+1=1+4+1=6
For x=0:
y=(0)2−4(0)+1=0−0+1=1
For x=1:
y=(1)2−4(1)+1=1−4+1=−2
For x=2:
y=(2)2−4(2)+1=4−8+1=−3
For x=3:
y=(3)2−4(3)+1=9−12+1=−2
For x=4:
y=(4)2−4(4)+1=16−16+1=1
For x=5:
y=(5)2−4(5)+1=25−20+1=6
Thus, the complete table is:
x
-1
0
1
2
3
4
5
y
6
1
-2
-3
-2
1
6
Step 2
Draw the graph of $y = x^2 - 4x + 1$ for $-1 \leq x \leq 5$
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Answer
To graph the quadratic function y=x2−4x+1 from x=−1 to x=5, we will plot the points calculated from the completed table. The points to plot are:
(−1,6)
(0,1)
(1,−2)
(2,−3)
(3,−2)
(4,1)
(5,6)
After plotting these points on the graph, draw a smooth curve through them. Ensure that the curve correctly represents the shape of a parabola, opening upwards.
