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 | | | | ... 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 this table of values for $y = x^2 + x - 4$
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Answer
To complete the table, we will substitute the given x-values into the equation y=x2+x−4.
For x=−3: y=(−3)2+(−3)−4=9−3−4=2
For x=−2: y=(−2)2+(−2)−4=4−2−4=−2
For x=−1: y=(−1)2+(−1)−4=1−1−4=−4
For x=0: y=(0)2+(0)−4=0−4=−4
For x=1: y=(1)2+(1)−4=1+1−4=−2
For x=2: y=(2)2+(2)−4=4+2−4=2
For x=3: y=(3)2+(3)−4=9+3−4=8
Thus the completed table is:
x
-3
-2
-1
0
1
2
3
y
2
-2
-4
-4
-2
2
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 from the completed table of values:
(-3, 2)
(-2, -2)
(-1, -4)
(0, -4)
(1, -2)
(2, 2)
(3, 8)
Draw a smooth curve that passes through these points to create a parabolic shape representing the quadratic function.
Step 3
Use the graph to estimate a solution to $x^3 + x - 4 = 0$
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Answer
From the graph, we look for the intersection points with the x-axis, which correspond to the solutions of the equation x3+x−4=0. Upon inspecting the graph, it appears that there is a root around x=1.6 based on where the curve intersects the x-axis.
