(a) Copy and complete the table of values for the relation \(y = 3x^{2} - 5x - 7\).
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
| y | 35 | -7 | -9 | 5 |
(b) Using scales of 2 cm to 1 unit on the x- axis and 2 cm to 5 units on the y- axis, draw the graph of \(y = 3x^{2} - 5x - 7, -3 \leq x \leq 4\).
(c) From the graph : (i) find the roots of the equation \(3x^{2} - 5x - 7 = 0\) ; (ii) estimate the minimum value of y ; (iii) calculate the gradient of the curve at the point x = 2.
(a)
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
| y | 35 | 15 | 1 | -7 | -9 | -5 | 5 | 21 |
(b) see graph above
(c) (i) The roots of the equation is where the graph cuts the x- axis = -0.9, 2.6.
(ii) Minimum value of y = -9.21
(iii) At x = 2,
gradient = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)
= \(\frac{4 - (-8.5)}{3.3 - 1.5}\)
= \(\frac{12.5}{1.8}\)
= 6.9444
\(\approxeq\) 6.9
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