Complete this table of values for $y = x^2 + x - 4$ - Edexcel - GCSE Maths - Question 3 - 2018 - Paper 3
Question 3
Complete this table of values for $y = x^2 + x - 4$.
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
|-----|----|----|----|----|----|----|----|
| y | -2 | -4 | 2 | -4... show full transcript
Worked Solution & Example Answer:Complete this table of values for $y = x^2 + x - 4$ - Edexcel - GCSE Maths - Question 3 - 2018 - Paper 3
Step 1
Complete the table of values
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Answer
To complete the table, substitute the values of x into the equation y=x2+x−4.
For x=−3: y=(−3)2+(−3)−4=9−3−4=2
The value is y=2.
For x=−2: y=(−2)2+(−2)−4=4−2−4=−2
The value is y=−2.
For x=−1: y=(−1)2+(−1)−4=1−1−4=−4
The value is y=−4.
For x=0: y=(0)2+(0)−4=0−4=−4
The value is y=−4.
For x=1: y=(1)2+(1)−4=1+1−4=−2
The value is y=−2.
For x=2: y=(2)2+(2)−4=4+2−4=2
The value is y=2.
For x=3: y=(3)2+(3)−4=9+3−4=8
The value is y=8.
Step 2
On the grid, draw the graph of $y = x^2 + x - 4$ for values of $x$ from -3 to 3
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Answer
Plot the points obtained from the table on a graph with x-values from -3 to 3 and corresponding y-values. Join the points smoothly to depict the curve of the quadratic function. Ensure that the curve reflects the parabolic nature of the equation, crossing the y-axis below -4.
Step 3
Use the graph to estimate a solution to $x^3 + x - 4 = 0$
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Answer
Observe the point where the curve of y=x2+x−4 intersects the x-axis. From the graph, we can estimate that the solution for the equation x3+x−4=0 occurs approximately at xext(around1.5). This is where the value of y becomes 0.
