Solve y=-7x² > 0: Finding Values Where Function is Positive

Given the function y=7x2 y=-7x^2

Determine for which values of x the following holds:

f(x)>0 f\left(x\right) > 0

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the function y=7x2 y=-7x^2

Determine for which values of x the following holds:

f(x)>0 f\left(x\right) > 0

2

Step-by-step solution

To solve this problem, let's work through the following steps:

Step 1: Analyze the inequality 7x2>0 -7x^2 > 0 .
Since x20 x^2 \geq 0 for all real x x and x2=0 x^2 = 0 when x=0 x = 0 , we know x2>0 x^2 > 0 when x0 x \neq 0 . However, the expression 7x2 -7x^2 is always less than or equal to zero because multiplying a non-negative x2 x^2 by 7-7 gives a non-positive result.
Therefore, 7x2>0 -7x^2 > 0 cannot be true for any real x x .

Step 2: Conclude based on this analysis.
The only scenario where 7x2 -7x^2 could have been greater than zero is if we had a positive term offsetting it, which is not the case.
Hence, there are no values of x x for which f(x)>0 f(x) > 0 .

The correct answer based on the provided choices is No x.

3

Final Answer

x0 x\ne0

Practice Quiz

Test your knowledge with interactive questions

The graph of the function below intersects the X-axis at points A and B.

The vertex of the parabola is marked at point C.

Find all values of \( x \) where \( f\left(x\right) > 0 \).

AAABBBCCCX

🌟 Unlock Your Math Potential

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

More Questions

Click on any question to see the complete solution with step-by-step explanations