Question

Find the $x$ - and $y$ -intercepts. $$ x=y^{2}-4 $$

   Find the $x$ - and $y$ -intercepts.
$$
x=y^{2}-4
$$

College Algebra Essentials

College Algebra Essentials

Julie Miller 1st Edition

Chapter 2, Problem 62

Instant Answer

Solved by Expert Erika Bustos

08/08/2021

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So, we have: $$x = 0^{2} - 4 = -4$$ Show more…

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Find the $x$ - and $y$ -intercepts. $$ x=y^{2}-4 $$

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Key Concepts

Intercepts

Intercepts are the points where a graph intersects the coordinate axes. The x-intercept is found by setting the y-coordinate to zero, while the y-intercept is determined by setting the x-coordinate to zero. These points provide valuable information about the graph's location and behavior relative to the coordinate axes.

Solving Equations

Finding intercepts involves solving equations by substituting specific values into the given equation. In the context of intercepts, this means replacing one variable with zero and then solving for the other variable, a fundamental practice in algebra that simplifies the process of finding key points on a graph.

Quadratic Relationships

Many graphs involve quadratic relationships, where one variable is squared. Understanding quadratic equations is essential because they may yield multiple intercepts and exhibit symmetry. When one variable is expressed as a quadratic function of another, identifying intercepts often requires solving a quadratic equation, which can involve factoring or applying other methods to find solutions.

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