In case of a quadratic function, why are there two x-intercepts and one y-intercept?

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- Aug 17th 2005, 08:23 PMAngel007Math question?
In case of a quadratic function, why are there two x-intercepts and one y-intercept?

- Aug 17th 2005, 10:46 PMrgep
You're talking about the graph of a quadratic function of the form y = ax^2 + bx +c. The x-intercept is the intersection of this graph with the x-axis, which is the line y=0. Putting y=0 in your equation gives you a quadratic ax^2+bx+c = 0 which has two roots in general. The y-intercept is the intersection of your graph with the y-axis, which is the line x=0. Putting x=0 gives you just y=c which is an equation giving you just one value of y. In summary then, the degree of your equation in x is two: the highest power of x you see is x^2, and there are two x-intercepts. The degree in y is one: the highest power of y you see is y which is y^1, and there is one y-intercept. Consider what you should expect from a cubic function y = ax^3 + bx^2 + cx + d and try some examples!