Theory question 113
Graphs of Functions(a) Copy and complete the following table of values for the relation y = 2x2 − 7x − 3
x: −2, −1, 0, 1, 2, 3, 4, 5
y: 19, , −3, , −9, , ,
(b) Using 2cm to 1 unit on the x-axis and 2cm to 5 units on the y-axis, draw the graph of y = 2x2 − 7x − 3 for −2 ≤ x ≤ 5 (c) From your graph, find the: (i) minimum value of y; (ii) gradient of the curve at x = 1 (d) By drawing a suitable straight line, find the values of x for which 2x2 − 7x − 5 = x + 4.
Show the model answer
(a) x = −1: 6; x = 1: −8; x = 3: −6; x = 4: 1; x = 5: 12.
(b) Plot and join with a smooth U-shaped curve.
(c)(i) Minimum y ≈ −9.1 (at x ≈ 1.75).
(ii) Tangent at (1, −8): gradient ≈ −3.
(d) 2x2 − 7x − 5 = x + 4 is the same as 2x2 − 7x − 3 = x + 6. Draw y = x + 6; it meets the curve at x ≈ −0.9 and x ≈ 4.9.
Rearrange so one side is exactly the drawn curve; the other side is the line to draw.