Q. 10 - Precalculus Enhanced with Graphing Utilities

Question

True or False If the discriminant $b^2-4ac=0$, the graph of $f\left(x\right)=a{x}^2+bx+c,a\ne 0$, will touch the x-axis at its vertex.

Step-by-Step Solution

Answer

The given statement is true.

Step 1. Given information.

The given statement is:

If the discriminant $b^2-4ac=0$, the graph of $f\left(x\right)=a{x}^2+bx+c,a\ne 0$, will touch the x-axis at its vertex.

Step 2. Determine whether the given statement is true or false.

If the discriminant $b^2-4ac>0$, the graph of $f\left(x\right)=a{x}^2+bx+c,a\ne 0$, will touch the x-axis twice.

If the discriminant $b^2-4ac=0$, the graph of $f\left(x\right)=a{x}^2+bx+c,a\ne 0$, will touch the x-axis at one point and that point is its vertex.

If the discriminant $b^2-4ac<0$, the graph of $f\left(x\right)=a{x}^2+bx+c,a\ne 0$, will not touch the x-axis.

Step 3. Conclusion.

The given statement is true.