Theory question 109
Graphs of Functions(a) Copy and complete the following table for the relation y = 5/2 + x − 4x2
x: −2.0, −1.5, −1.0, −0.5, 0, 0.5, 1, 1.5, 2
y: −15.5, , , 1, 2.5, , , ,
(b) Using a scale of 2cm to 1 unit on the x axis and 2cm to 5 units on the y axis, draw the graph of the relation for −2.0 ≤ x ≤ 2.0
(c) What is the maximum value of y?
(d) From your graph obtain the roots of the equation 8x2 − 2x − 5 = 0.
Show the model answer
(a) y values: x = −2.0 → −15.5; −1.5 → −8; −1.0 → −2.5; −0.5 → 1; 0 → 2.5; 0.5 → 2; 1 → −0.5; 1.5 → −5; 2 → −11.5
(b) Plot the points with the given scales and join them with a smooth n-shaped curve.
(c) Maximum y ≈ 2.6 (exact value 2.5625 at x = 0.125)
(d) 8x2 − 2x − 5 = 0 is −2 times (5/2 + x − 4x2) = 0, i.e. y = 0
Read where the curve cuts the x-axis: x ≈ −0.7 and x ≈ 0.9 (exact −0.68 and 0.93)
Dividing 8x² − 2x − 5 = 0 by −2 gives exactly the plotted relation set to zero.