(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.
Explanation
(a)
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
| y | 35 | 15 | 1 | -7 | -9 | -5 | 5 | 21 |
(b)
(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