What can be inferred about the roots of a quadratic function if its graph does n

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Question: What can be inferred about the roots of a quadratic function if its graph does not intersect the x-axis?

Options:

Correct Answer: It has no real roots.

Solution:

If the graph of a quadratic function does not intersect the x-axis, it indicates that the function has no real roots.

What can be inferred about the roots of a quadratic function if its graph does not intersect the x-axis?

What can be inferred about the roots of a quadratic function if its graph does not intersect the x-axis?

Step 1: Understand what a quadratic function is. It is a function that can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants.
Step 2: Know that the graph of a quadratic function is a parabola. It can open upwards or downwards depending on the value of 'a'.
Step 3: The x-axis is the horizontal line where y = 0. If the graph of the quadratic function does not touch or cross this line, it means there are no points where f(x) = 0.
Step 4: Real roots of a function are the x-values where the graph intersects the x-axis. If the graph does not intersect the x-axis, it means there are no real roots.
Step 5: Therefore, if the graph of a quadratic function does not intersect the x-axis, we can conclude that the function has no real roots.

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