J17

From the graphs,
(a) Maximum value of 1 + x – 2x 2 ≈ 1.1
(b) Values of x where the straight line intersects the curve are x = -2 and
x = 1.5. At these points both 1 + x – 2x 2 and 2x – 5 are equal.
Hence 1 + x – 2x 2 = 2x – 5
1 + 5 + x – 2x – 2x 2 = 0
6 – x – 2x 2 = 0
Or 2x 2 + x – 6 = 0
Solutions of 2x 2 + x – 6 = 0 are x = -2 and x = 1.5
Exercise
1. Draw the graph of y = x 2 – 4x + 4 for values of x from -1 to +5. Solve from your
graph the equations:
(a) x 2 – 4x + 4 = 0 (b) x 2 – 4x + 1 = 0,
(c) x 2 – 4x – 1 = 0.
2. Draw the graph of the function x 2 – 6x + 5 for -1 ≤ x ≤ 7. Find the least value of this
function and the corresponding value of x. Use your graph to solve the equations:
(a) x 2 – 6x + 5 = 0 (b) x 2 – 6x = 1.
3. Draw the graph of y = 2x 2 – 7x – 2 for values of x from -3 to +3. State the least value
of y and the corresponding value of x. Use your graph to solve the equations:
(a) 2x 2 – x = 4, (b) 2x 2 – x + 6 = 0,
(c) 2x 2 – x – 4 = 2x.
4. Draw the curve of y =
draw the curve of y =
1
4
1
2
x
2
x
4
for domain -4 ≤ x ≤ 4. Using the same scale and axes,
-3.