Complete this table for $y = x^2 - 3$ - OCR - GCSE Maths - Question 21 - 2021 - Paper 1
Question 21
Complete this table for $y = x^2 - 3$.
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
|----|----|----|----|---|---|---|---|
| y | 6 | 1 | -2 | -3 | -2 | 1 | 6 |
Draw t... show full transcript
Worked Solution & Example Answer:Complete this table for $y = x^2 - 3$ - OCR - GCSE Maths - Question 21 - 2021 - Paper 1
Step 1
Complete this table for $y = x^2 - 3$
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Answer
To complete the table, we calculate the value of y for each value of x using the equation y=x2−3:
For x=−3: y=(−3)2−3=9−3=6
For x=−2: y=(−2)2−3=4−3=1
For x=−1: y=(−1)2−3=1−3=−2
For x=0: y=(0)2−3=0−3=−3
For x=1: y=(1)2−3=1−3=−2
For x=2: y=(2)2−3=4−3=1
For x=3: y=(3)2−3=9−3=6
Thus, the completed table is:
x
-3
-2
-1
0
1
2
3
y
6
1
-2
-3
-2
1
6
Step 2
Draw the graph of $y = x^2 - 3$ for values of $x$ from -3 to 3
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Answer
To draw the graph, plot the points from the completed table:
Plot (−3,6)
Plot (−2,1)
Plot (−1,−2)
Plot (0,−3)
Plot (1,−2)
Plot (2,1)
Plot (3,6)
Connect these points with a smooth curve, which shows that the graph is a parabola opening upwards.
Step 3
Use your graph to solve $x^2 - 3 = 2$
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Answer
To solve x2−3=2, we first rearrange this equation to x2=5.
From the graph, find where the curve intersects the line y=2. The points of intersection will provide the solutions for x. The approximate solutions are:
