Finding the intercepts of an equation

Finding the intercepts of an equation makes it easier to sketch the graph of the equation.  The graph of some functions can have one intercept, more than one intercept or no intercepts. 

On the Cartesian Coordinate Plane, there are two types of intercepts.   

The point where the graph crosses the x-axis is called the x-intercept.  The value of y is 0.  The x coordinate can be found by replacing y with 0 in the equation and solving for x. 

A linear equation is a straight line.  A vertical line has one x-intercept and the equation of a vertical line is x = a.  A horizontal line has no x-intercept.  The equation of a horizontal line is y = b.  A linear equation in the form y = mx + b has one x-intercept and one y-intercept.

A quadratic equation has a graph in the shape of a parabola.  A quadratic equation can have one, two or no x-intercepts. 

A cubic equation will have one, two or three x-intercepts.

The point where the graph crosses the y-axis is called the y-intercept.  The value of x is 0.  The y coordinate can be found by replacing x with 0 in the given equation and solving for y.

A linear equation in the form y = mx + b the value of b is the y-intercept.  When x = 0, y = m(0) + b or y = b.  The y-intercept is the point (0,b).

Filed under: Functions and Their Graphs

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