Theory question 113
Graphs of FunctionsThe table shows the values of the relation y = 11 − 2x − 2x2 for −4 ≤ x ≤ 3
x: −4, −3, −2, −1, 0, 1, 2, 3
y: −13, , , , 11, , ,
(a) Copy and complete the table (b) Using a scale of 2cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of y = 11 − 2x − 2x2. (c) Use your graph to find: (i) the roots of the equation 11 − 2x − 2x2 = 0, (ii) the values of x for which 3 − 2x − 2x2 = 0, (iii) the gradient of the curve at x = 1
Show the model answer
(a) x = −3: −1; −2: 7; −1: 11; 1: 7; 2: −1; 3: −13.
(b) Plot the points and join with a smooth upside-down parabola.
(c)(i) The curve crosses y = 0 at x ≈ −2.9 and x ≈ 1.9.
(ii) 3 − 2x − 2x2 = 0 means 11 − 2x − 2x2 = 8; draw y = 8: x ≈ −1.8 and x ≈ 0.8.
(iii) Draw the tangent at (1, 7); its gradient is about −6.
Add 8 to both sides of the new equation so it matches the drawn curve.