Look at the function below:
Then determine for which values of the following is true:
We have hundreds of course questions with personalized recommendations + Account 100% premium
Look at the function below:
Then determine for which values of the following is true:
To solve this problem, we'll follow these steps:
Step 1: We are given the function . This is a quadratic function expressed as a square of a linear term.
Step 2: Consider the expression . Whatever value this linear expression takes, its square, , will always be non-negative. This is because the square of a real number is never negative.
Step 3: To find when , we realize that since squares are non-negative, they cannot actually be negative. Thus, for all values of , and can never be less than zero.
Therefore, no value of will make .
The conclusion is that there is no value of for which .
No value of
The graph of the function below does not intersect the \( x \)-axis.
The parabola's vertex is marked A.
Find all values of \( x \) where
\( f\left(x\right) > 0 \).
When you multiply any real number by itself, the result is always zero or positive. For example: and . Even negative numbers become positive when squared!
It means the inequality cannot be satisfied by any real number. Since is never negative, there's no value of x that makes it less than zero.
Yes! when , so . But the question asks for when it's less than zero, which never happens.
Look for squared expressions being compared to negative numbers. Since squares are never negative, inequalities like or have no solutions.
Then almost all real numbers would work! is true for all x except where the expression equals zero.
Get unlimited access to all 18 The Quadratic Function questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime