Question

If a graph of a quadratic function can have 0, 1 or 2 x-intercepts. How can you predict the number of x-intercepts without drawing the graph or (completely) solving the related equation?

Suppose that the graph of f(x) = ax^2+bx+c has x-intercepts (m,0) and (n,0). What are the x-intercepts of g(x) = –ax^2–bx–c?

I really don't understand this, any elaboration will be greatly appreciated. thank in advance

Answer 1

look at
b^2 - 4 a c

if +, then two intercepts
if 0, then just grazes the x axis, one intercept
if -, then never hits the axis, imaginary roots only

if a x^2 + b x + c = 0
then
- (a x^2 + b x + c) = 0
is the same because +0 = -0