Q. 8 - Precalculus Enhanced with Graphing Utilities

Question

True or False The graph of $f\left(x\right)=2x^2+3x-4$ opens up.

Step-by-Step Solution

Answer

The given statement is true.

Step 1. Given information.

The given function is:

$f\left(x\right)=2x^2+3x-4$

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

The graph of the function $f\left(x\right)=a{x}^2+bx+c$ opens up if $a>0$ and opens down if $a<0$.

In the given function $f\left(x\right)=2x^2+3x-4$, $a=2>0$. So, the graph of the function opens up.

Step 3. Conclusion.

The given statement is true.