(a) Copy and complete the following table of values for \(y = 2x^{2} - 9x - 1\). x -1 0 1 2 3 4 5 6 y -1 -8 -11 17 (b) Using a scale of 2cm to represent 1 u...
Question 1 Report
(a) Copy and complete the following table of values for \(y = 2x^{2} - 9x - 1\).
| x | -1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| y | -1 | -8 | -11 | 17 |
(b) Using a scale of 2cm to represent 1 unit on the x- axis and 2cm to represent 5 units on the y- axis, draw the graph of \(y = 2x^{2} - 9x - 1\).
(c) Use your graph to find the : (i) roots of the equation \(2x^{2} - 9x = 4\), correct to one decimal place ; (ii) gradient of the curve \(y = 2x^{2} - 9x - 1\) at x = 3.
Answer Details
(a) Completing the table for \(y = 2x^{2} - 9x - 1\).
- \(x=-1:\ 2(1)-9(-1)-1 = 2+9-1 = 10\)
- \(x=3:\ 2(9)-9(3)-1 = 18-27-1 = -10\)
- \(x=4:\ 2(16)-9(4)-1 = 32-36-1 = -5\)
- \(x=5:\ 2(25)-9(5)-1 = 50-45-1 = 4\)
| \(x\) | -1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|---|
| \(y\) | 10 | -1 | -8 | -11 | -10 | -5 | 4 | 17 |
(b) Plot the points and join with a smooth parabola.
(c)(i) Roots of \(2x^{2} - 9x = 4\). Since \(y = 2x^{2}-9x-1\), rewrite \(2x^{2}-9x-4=0\) as \(2x^{2}-9x-1 = 3\). Draw the line \(y = 3\) and read where it cuts the curve:
\[x = \frac{9 \pm \sqrt{81+32}}{4} = \frac{9 \pm 10.63}{4} \;\Rightarrow\; x \approx -0.4 \text{ or } 4.9\](c)(ii) Gradient at \(x = 3\). Draw a tangent at \(x=3\); its slope is
\[\frac{dy}{dx} = 4x - 9 = 4(3) - 9 = \mathbf{3}\]Download The App On Google Playstore
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