Question

State the circumstances that cause the graph of a quadratic function $f\left(x\right)=a{x}^2+bx+c$to have no x-intercepts.

Short answer

The graph does not have x-intercept when$b^2-4ac<0$

Step-by-step solution

Given information

We are given a quadratic equation of the form$f\left(x\right)=a{x}^2+bx+c$

Explanation

We know that discriminant of a quadratic equation $a{x}^2+bx+c$is given by $b^2-4ac$.When$b^2-4ac<0$then the graph of the function does not intersect x-axis. Hence the function has no x-intercept when $b^2-4ac<0$