Graphs of Linear & Quadratic Functions

a. Copy and complete the tables of values of y = \(2x^2 - x - 4\) for -3 ≤ x ≤ 3 x -3 -2 -1 0 1 2 3 y 17 -4 b. Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 unit on the y-axis, draw the graph of y = \(2x^2 - x - 4\) for -3 ≤ x ≤ 3. ci. Use the graph to find: the roots of the equation \(2x^2 - x - 4\) ii. Use the graph to find the: values of x for which y increases as x increases; iii. Use the graph to find the: minimum point of y.

(a) Copy and complete the table of values for the relation y=2x\(^2\) - x - 2 for 4 ≤ x ≤ 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 ≤ x ≤ 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-3r-5 0; (i) range of values of x for which 2x\(^2\) -x - 2<0.

The graph of the equations y = 2x + 5 and y = 2x\(^2\) + x - 1 are shown. Use the information above to answer this question. Find the point of intersection of the two graphs.

The graph of the equations y = 2x + 5 and y = 2x\(^2\) + x - 1 are shown. Use the information above to answer this question. If x = -2.5, what is the value of u on the curve?

(a) (i) Using a scale of 2 cm to 1 unit on both axes, on the same graph sheet, draw the graphs of \(y - \frac{3x}{4} = 3\) and \(y + 2x = 6\). (ii) From your graph, find the coordinates of the point of intersection of the two graphs. (iii) Show, on the graph sheet, the region satisfied by the inequality \(y - \frac{3}{4}x \geq 3\). (b) Given that \(x^{2} + bx + 18\) is factorized as \((x + 2)(x + c)\). Find the values of c and b.