Power of Maths: Paper 1 – Section 7 (c) b2 − 4ac < 0 ⇒ b2 < 4ac
This means there are no real roots. (They are complex.) The graph of y = ax2 + bx + c does not cross the x-axis at any point.
a > 0 y
a < 0 y
(0, c)
x or
(0, c)
x
y = 2x2 – 4x + 5 b2 – 4ac = 16 – 40 = –24 < 0 Beacause b2 < 4ac, the graph of the function does not cross the x-axis. It crosses the y-axis at (0, 5).
3. Finding the maximum and minimum points (vertices or turning points) of a quadratic function Given the quadratic function y = ax 2 + bx + c, the maximum or minimum values of the function occur at x = − b
Differentiation. y
___ 2a . You will see why this is the case in Section 8:
Vertex or maximum a < 0
y a > 0
Vertex or minimum
x = – b
— 2a
x x = – b
— 2a
x
The vertex is the most important point on a quadratic graph.
