How many real zeros can a quadratic function have?
Understand the Problem
The question is asking about the possible real zeros of a quadratic function, which is a polynomial of degree two. The number of real zeros can be determined by the discriminant, which is part of the quadratic formula.
Answer
0, 1, or 2
Answer for screen readers
A quadratic function can have 0, 1, or 2 real zeros.
Steps to Solve
- Identify the standard form of a quadratic function
A quadratic function can be written in the form $ax^2 + bx + c$.
- Recall the quadratic formula
The quadratic formula for solving $ax^2 + bx + c = 0$ is $$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$
- Understand the discriminant
The discriminant is the part of the quadratic formula under the square root: $$ b^2 - 4ac $$
- Determine the condition for the number of real zeros
- If $b^2 - 4ac > 0$, there are two distinct real zeros.
- If $b^2 - 4ac = 0$, there is exactly one real zero (a repeated root).
- If $b^2 - 4ac < 0$, there are no real zeros (the zeros are complex).
A quadratic function can have 0, 1, or 2 real zeros.
More Information
The discriminant helps determine the number of real solutions for a quadratic function, providing insight into the nature of the function's graph.
Tips
A common mistake is misinterpreting the discriminant. Ensure you calculate $b^2 - 4ac$ correctly, and carefully interpret its sign to determine the number of real zeros.
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