Theory question 110
Graphs of Functions(a) Copy and complete the following table of values for y = 2x2 − 9x − 1.
x: −1, 0, 1, 2, 3, 4, 5, 6
y: __, −1, −8, −11, __, __, __, 17
(b) Using a scale of 2cm to represent 1 unit on the x-axis and 2cm to represent 5 unit on the y-axis, draw the graph of y = 2x2 − 9x − 1 for −1 ≤ x ≤ 6.
(c) Use your graph to find the: (i) roots of the equation 2x2 − 9x = 4, correct to one decimal place; (ii) gradient of the curve y = 2x2 − 9x − 1 at x = 3.
Show the model answer
(a) x = −1: y = 10; x = 3: y = −10; x = 4: y = −5; x = 5: y = 4
(b) Plot the points with the given scales and join with a smooth U-shaped curve.
(c)(i) 2x2 − 9x = 4 means 2x2 − 9x − 1 = 3: draw y = 3 and read x ≈ −0.4 and x ≈ 4.9
(ii) Draw the tangent at x = 3 and find rise ÷ run: gradient ≈ 3
Rewrite the new equation so its left side matches the graph; the right side is the horizontal line to draw.