Theory question 109
Graphs of Functions(a) Copy and complete the table below for y = 3x2 − 5x − 7
x: −3, −2, −1, 0, 1, 2, 3, 4
y = 3x2 − 5x − 7: 35, __, __, −7, −9, __, 5, __
(b) Using a scale of 2cm = 1 unit along the X-axis and 2cm = 5 units along the y-axis, draw the graph of y = 3x2 − 5x − 7. (c) On the same axis draw the graph of y + 3x + 2 = 0. (d) From your graph, find the: (i) range of values of x for which 3x2 − 5x − 7 < 0 (ii) roots of the equation 3x2 − 2x − 5 = 0.
Show the model answer
(a) x = −2: y = 15; x = −1: y = 1; x = 2: y = −5; x = 4: y = 21. Full row: 35, 15, 1, −7, −9, −5, 5, 21.
(b) Plot the points with the given scale and join them with a smooth U-shaped curve.
(c) y = −3x − 2: points such as (−3, 7), (0, −2), (4, −14); draw the straight line.
(d)(i) The curve is below the x-axis between where it crosses it: −0.9 < x < 2.6 (approximately).
(ii) 3x2 − 2x − 5 = 0 is the same as 3x2 − 5x − 7 = −3x − 2, so read the x-values where the curve meets the line: x = −1 and x ≈ 1.7 (exactly 5/3).
Rearrange the new equation so one side is the curve's expression; the other side is the line to draw.