Zeros

Definition

The zeros of a function are the values of the independent variable where the function equals zero. In the context of graphing quadratic functions, the zeros represent the x-intercepts of the parabola, which are the points where the graph crosses the x-axis.

5 Must Know Facts For Your Next Test

1. The number of zeros of a quadratic function depends on the sign of the discriminant, which is calculated as $b^2 - 4ac$.
2. If the discriminant is positive, the quadratic function has two real zeros. If the discriminant is zero, the function has one real zero. If the discriminant is negative, the function has no real zeros.
3. The zeros of a quadratic function can be used to determine the x-intercepts of the graph, which are the points where the parabola crosses the x-axis.
4. The zeros of a quadratic function can be used to determine the range of the function, which is the set of all possible output values.
5. The zeros of a quadratic function can be used to determine the domain of the function, which is the set of all possible input values.

Review Questions

• Explain how the zeros of a quadratic function relate to the x-intercepts of the graph.
  • The zeros of a quadratic function represent the values of the independent variable (x) where the function equals zero. These zeros correspond to the x-intercepts of the parabolic graph, which are the points where the graph crosses the x-axis. The number and location of the zeros determine the shape and position of the parabola on the coordinate plane.
• Describe how the discriminant of a quadratic function can be used to determine the number of real zeros.
  • The discriminant of a quadratic function, calculated as $b^2 - 4ac$, can be used to determine the number of real zeros of the function. If the discriminant is positive, the function has two real zeros. If the discriminant is zero, the function has one real zero. If the discriminant is negative, the function has no real zeros. This information is crucial for understanding the behavior and graphical representation of quadratic functions.
• Analyze how the zeros of a quadratic function can be used to determine the range and domain of the function.
  • The zeros of a quadratic function provide valuable information about the function's range and domain. The zeros represent the x-intercepts of the parabolic graph, which can be used to determine the domain of the function (the set of all possible input values). Additionally, the zeros, along with the vertex of the parabola, can be used to determine the range of the function (the set of all possible output values). Understanding the relationship between the zeros and the function's range and domain is essential for accurately graphing and analyzing quadratic functions.

Related terms

Vertex:

The point on a parabola where the graph changes direction, representing the minimum or maximum value of the function.

Axis of Symmetry:

The vertical line that passes through the vertex of a parabola, dividing the graph into two symmetric halves.

Quadratic Formula:

The formula used to find the zeros of a quadratic function, given in the form $ax^2 + bx + c = 0$.