Question

Which one of the following is TRUE for the function \( y = x^2 + 1 \)?

• A. It does not intersect the X-axis at all
• B. It intersects the X-axis at \( x = -1 \)
• C. It intersects the X-axis at \( x = +1 \)
• D. It is tangential to the X-axis

Hint:

For a quadratic function \( y = ax^2 + b \), if the constant term is positive, the graph does not intersect the X-axis.

Answer 1

The Correct Option is A

Step 1: Understanding the function.
The given function is a quadratic equation \( y = x^2 + 1 \). To find where it intersects the X-axis, set \( y = 0 \).
Step 2: Solve the equation.
Setting \( y = 0 \) gives the equation \( 0 = x^2 + 1 \). This simplifies to \( x^2 = -1 \), which has no real solution because \( x^2 \geq 0 \) for all real values of \( x \).
Step 3: Conclusion.
Thus, the graph does not intersect the X-axis at all, making the correct answer (A).