5 (a) Complete the table of values for $y = x^2 - x - 6$ - Edexcel - GCSE Maths - Question 6 - 2018 - Paper 2
Question 6
5 (a) Complete the table of values for $y = x^2 - x - 6$.
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
|----|----|----|----|---|---|---|---|
| y | 6 | 4 | 2 | -6 | -6 ... show full transcript
Worked Solution & Example Answer:5 (a) Complete the table of values for $y = x^2 - x - 6$ - Edexcel - GCSE Maths - Question 6 - 2018 - Paper 2
Step 1
Complete the table of values for $y = x^2 - x - 6$
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Answer
To complete the table, we calculate the corresponding y values for each x:
For x=−3:
y=(−3)2−(−3)−6=9+3−6=6
For x=−2:
y=(−2)2−(−2)−6=4+2−6=0
For x=−1:
y=(−1)2−(−1)−6=1+1−6=−4
For x=0:
y=02−0−6=−6
For x=1:
y=12−1−6=1−1−6=−6
For x=2:
y=22−2−6=4−2−6=−4
For x=3:
y=32−3−6=9−3−6=0
The completed table is:
x
-3
-2
-1
0
1
2
3
y
6
0
-4
-6
-6
-4
0
Step 2
On the grid, draw the graph of $y = x^2 - x - 6$ for values of $x$ from -3 to 3
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Answer
To graph the equation, plot the points obtained in part (a) on the graph with x values from -3 to 3. Connect these points with a smooth curve, ensuring it is parabolic in shape. The correct shape will show the characteristic curvature of a quadratic function.
Step 3
Use your graph to find estimates of the solutions to the equation $x^2 - x - 6 = -2$
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Answer
To estimate the solutions, rewrite the equation as:
x2−x−4=0
Find the points where y=x2−x−6 intersects the line y=−2. Based on the graph, these intersections appear to occur approximately at x=−1 and x=3. Thus, the estimated solutions to the equation are around these x values.
