Fill in each blank with the appropriate word or phrase....

Fill in each blank with the appropriate word or phrase. Carefully reread the section if needed.
If the leading coefficient is positive and the vertex $(h, k)$ is in Quadrant IV, the graph will have _____ $x$ -intercepts.

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Key Concepts

Quadratic Functions

A quadratic function is a second-degree polynomial that can be represented in standard form as ax² + bx + c or in vertex form as a(x - h)² + k. The properties of the quadratic function, including its vertex, axis of symmetry, and intercepts, are essential in understanding its graph and behavior.

Leading Coefficient

The leading coefficient, represented by 'a' in a quadratic function, determines the direction in which the parabola opens. When a is positive, the parabola opens upward, meaning that the vertex represents the minimum point of the function and significantly influences the number and nature of x-intercepts.

Vertex

The vertex of a quadratic function is the point (h, k) where the function reaches its maximum or minimum value, depending on whether the parabola opens downward or upward. The position of the vertex relative to the x-axis can provide insight into whether the parabola will intersect the x-axis and, if so, how many times.

X-intercepts

X-intercepts are the points where a graph crosses the x-axis, corresponding to the solutions of the equation when the function is set to zero. In the context of quadratic functions, the number of x-intercepts is influenced by both the leading coefficient and the location of the vertex, as well as the discriminant in the quadratic formula.

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