Complete the table of values for $y = x^2 - x - 6$ - Edexcel - GCSE Maths - Question 11 - 2018 - Paper 2
Question 11
Complete the table of values for $y = x^2 - x - 6$.
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| y | 6 | | | | | | |
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Worked Solution & Example Answer:Complete the table of values for $y = x^2 - x - 6$ - Edexcel - GCSE Maths - Question 11 - 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 need to calculate the value of y for each corresponding value of x. We take the function y=x2−x−6 and evaluate it for each x from -3 to 3:
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=(0)2−(0)−6=0−0−6=−6
For x=1: y=(1)2−(1)−6=1−1−6=−6
For x=2: y=(2)2−(2)−6=4−2−6=−4
For x=3: y=(3)2−(3)−6=9−3−6=0
Thus, 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
Once the values have been tabulated, plot the points on the Cartesian plane using the calculated values of y. The points to plot are:
(−3,6)
(−2,0)
(−1,−4)
(0,−6)
(1,−6)
(2,−4)
(3,0)
Connect these points with a smooth curve to represent the graph of the quadratic function, noting that it opens upwards. Ensure that the vertex and any intercepts are clear on your graph.
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 find the solutions for the equation x2−x−6=−2, we can rearrange this to x2−x−4=0. This means we are looking for the x-values where the graph intersects the line y=−2. By looking at the graph, find the approximate points of intersection. The estimates can be directly read from the graph:
One solution is around xext(approxiamtely−1.5).
Another solution is around xext(approximately2.5).
Therefore, the estimates for the solutions are approximately xextvaluesintherangeof[−1.5,2.5].
