Graphing Quadratic Functions and Solving Equations
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7 (a) Copy and complete the table of values for the relation $y=2x^{2} - x - 2$ for $-4 \leq x \leq 4$.
| x | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|---|---|---|
| y | | 19 | | | -2 | | | | 26 |
(b) Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of $y = 2x^{2} - x - 2$ for $-4 \leq x \leq 4$.
(c) On the same axes, draw the graph of $y = 2x + 3$.
(d) Use the graph to find the: (i) roots of the equation $2x^{2} - 3x - 5 = 0$; (ii) range of values of x for which $2x^{2} - x - 2 < 0$.
This question includes visual content: The image displays a two-row table with 9 columns for x values from -4 to 4 and corresponding y values. The x-row includes the values -4, -3, -2, -1, 0, 1, 2, 3, 4. The y-row has 19 under -4, -2 under 0, and 26 under 4, with empty boxes for the others.
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Hi Martin, let's solve this quadratic graphing problem. We'll start by completing the table of values for the relation y equals two x squared minus x minus two.
Part (a): Table of Values
We need to calculate y for the missing x values ranging from negative four to four.
| x | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|---|---|---|
| y | 19 | -2 | 26 |
When x is negative four, y is two times negative four squared, minus negative four, minus two. Calculating that gives us thirty-two plus four minus two, which is thirty-four.
For x equals negative two, we get eight plus two minus two, which equals eight.
When x is negative one, we have two plus one minus two, resulting in one.
For x equals one, we get two minus one minus two, which is negative one.
For x equals two, we get eight minus two minus two, which is four.
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