Question

The graph of the polynomial f(x) = ax² + bx + c is as shown below. Write the signs of 'a' and b² − 4ac.

Answer 1

Clearly, f(x) = ax² bx + c represent a parabola opening upwards. Therefore, `a > 0`

Since the parabola cuts x-axis at two points, this means that the polynomial will have two real solutions

Hence, b² - 4ac > 0

Hence, a > 0 

x = 0

F(0) = a × 0 + b × 0 + c

y = c

c > 0

c → positive