X-Intercepts - Varsity Tutors

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x-Intercepts

Study Guide

Key Definition

The x-intercepts of a function are the point(s) where the graph of the function crosses the x-axis. This can be represented as $(x, 0)$.

Important Notes

  • The x-intercept is where the graph crosses the x-axis.
  • For a quadratic function $ax^2 + bx + c = 0$, the x-intercepts are the solutions to the equation.
  • In a linear equation $y = mx + b$, the x-intercept is found by setting $y = 0$.
  • If a graph does not cross the x-axis, it has no x-intercepts.
  • The x-intercept is often referred to just by its x-value.
  • For a rational function, set the numerator = 0 provided the denominator ≠ 0.

Mathematical Notation

Remember to use proper notation when solving problems

Why It Works

The x-intercept is found by setting the function equal to zero $f(x) = 0$, which gives the x-value where the graph crosses the x-axis.

Remember

To find x-intercepts, solve for $x$ when $y = 0$.

Quick Reference

Property:$f(x) = 0$

Understanding x-Intercepts

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Video explanation of this concept

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Beginner Explanation

An x-intercept is the point where a graph crosses the x-axis, represented as $(x, 0)$.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

What is the x-intercept of the equation $y = 2x - 4$?

A$x = 2$B$x = 4$C$x = -2$D$x = 0$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

A skateboarder jumps off a ramp, and their height is modeled by $h(t) = -5t^2 + 20t + 5$. Find the time when they are at ground level.Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Consider the function $f(x) = x^3 - 6x^2 + 11x - 6$. What are the x-intercepts?

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

Find the x-intercepts of $f(x) = x^2 - 4x + 4$.

A$x = 2 (multiplicity 2)$B$x = 2$C$x = -2$D$x = 4$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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Review key concepts and takeaways

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