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Complete this table of values for y = x² + x − 4 for values of x from -3 to 3 - Edexcel - GCSE Maths - Question 4 - 2018 - Paper 3
Question 4
Complete this table of values for y = x² + x − 4 for values of x from -3 to 3. x −3 −2 −1 0 1 2 3 y −2 −4 −2 On the grid... show full transcript
Worked Solution & Example Answer:Complete this table of values for y = x² + x − 4 for values of x from -3 to 3 - Edexcel - GCSE Maths - Question 4 - 2018 - Paper 3
Step 1
Complete this table of values for y = x² + x − 4 for values of x from -3 to 3.
Answer
To complete the table, we calculate y for each x value:
-
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 = 0² + 0 - 4 = 0 - 4 = -4
-
For x = 1:
y = 1² + 1 - 4 = 1 + 1 - 4 = -2
-
For x = 2:
y = 2² + 2 - 4 = 4 + 2 - 4 = 2
-
For x = 3:
y = 3² + 3 - 4 = 9 + 3 - 4 = 8
The completed table is:
| x | y |
|---|---|
| -3 | 2 |
| -2 | -2 |
| -1 | -4 |
| 0 | -4 |
| 1 | -2 |
| 2 | 2 |
| 3 | 8 |
Step 2
On the grid, draw the graph of y = x² + x − 4 for values of x from -3 to 3.
Answer
To draw the graph based on the values computed:
- Mark the points from the completed table on the grid.
- Connect the points with a smooth curve, ensuring the graph reflects the quadratic nature of the function.
- Make sure to accurately represent the minimum point below y = -4.
Step 3
Use the graph to estimate a solution to x³ + x − 4 = 0.
Answer
To estimate the solution to the equation x³ + x − 4 = 0 using the graph:
- Look for the points where the graph intersects the x-axis.
- By observing the graph, estimate the x-value at which y=0. For instance, one may estimate that x is approximately between 1.6 and 2.0.