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 complementary value of x given in the table.
Calculate y when x=0:
y=02−4(0)+1=1
Calculate y when x=1:
y=12−4(1)+1=1−4+1=−2
Calculate y when x=2:
y=22−4(2)+1=4−8+1=−3
Calculate y when x=3:
y=32−4(3)+1=9−12+1=−2
Calculate y when x=4:
y=42−4(4)+1=16−16+1=1
Calculate y when x=5:
y=52−4(5)+1=25−20+1=6
Thus, the completed 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 $-1 < x < 5$
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Answer
To draw the graph for the function y=x2−4x+1 over the interval −1<x<5, we first plot the points calculated in the previous step.
Plot the points:
(−1,6)
(0,1)
(1,−2)
(2,−3)
(3,−2)
(4,1)
(5,6)
Connect these points with a smooth curve since this is a quadratic function.
Ensure that the curve is continuous and reflects the parabolic nature typical of quadratic functions, demonstrating a minimum point at x=2 (the vertex).
