**Question:**1. What is an x-intercept of the graph of a quadratic function? How many possible x-intercepts does the graph of a quadratic function have? Explain.---**Explanation:**An **x-intercept** is a point where the graph of a function crosses the x-axis. For a quadratic function, which is typically in the form $ ax^2 + bx + c = 0 $, the x-intercepts are the values of $ x $ that make the equation equal to zero.A quadratic function can have:- **Two x-intercepts**: This occurs when the quadratic equation has two distinct real roots. The graph of the quadratic function will intersect the x-axis at two points. - **One x-intercept**: This happens when the quadratic equation has exactly one real root (i.e., a "double root"). The graph will touch the x-axis at just one point, indicating the vertex of the parabola is on the x-axis. - **No x-intercepts**: This is the case when there are no real roots, meaning the solutions are complex numbers. Here, the graph does not cross or touch the x-axis at any point.These scenarios are determined by the discriminant $ b^2 - 4ac $ from the quadratic formula $\frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}$:- If $ b^2 - 4ac > 0 $, there are two distinct real roots.- If $ b^2 - 4ac = 0 $, there is one real root.- If $ b^2 - 4ac < 0 $, there are no real roots.

Answered: 1. What is an x-intercept of the graph…

1. What is an x-intercept of the graph of a quadratic function? How many possible x-intercepts does the graph of a quadratic function have? Explain?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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