Q. 101 - Precalculus Enhanced with Graphing Utilities

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.

Step-by-Step Solution

Answer

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

Step 1: Given information

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

Step 2: 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 $b^2-4ac<0$