Intercepts of Quadratic FunctionsDate: 12/10/2003 at 00:24:29 From: Terri Subject: Quadratic Functions In some quadratic functions, why are there two x-intercepts and one y- intercept? Date: 12/10/2003 at 07:17:55 From: Doctor Dotty Subject: Re: Quadratic Functions Hi Terri, Thanks for the question. The following is a graph of a quadratic function with two x- intercepts and one y-intercept: \ | \ | \ | / \ | / \ | .' \ | ' '. | / `. | / | | / \| / . / |`. / | \ / | \ ,' ------------+----`.------------------,------------- | `. ,' | `._ ,' | `--._,-'' | | | | No function can have more than one y-intercept, because for any function each input maps onto no more than one output. If there were two y-intercepts, it would mean that a single value of x (i.e., x=0) maps onto two distinct values of y. I don't know whether you are familiar with the quadratic equation, Whenever ax^2 + bx + c = 0, -b +/- sqrt(b^2 - 4ac) x = ------------------------ 2a When the quantity b^2 - 4ac is equal to zero, x has only one real value, corresponding to the case where the function intercepts the x-axis in only one place. When b^2 - 4ac is less than zero, x has no real values, corresponding to the case where the function doesn't intercept the x-axis at all. But when b^2 - 4ac is greater than zero, x has two real values, each of which corresponds to one of its x-intercepts. Write back if I can be of any more help--on this or anything else. - Doctor Dotty, The Math Forum http://mathforum.org/dr.math/ Date: 12/11/2003 at 00:03:38 From: Terri Subject: Thank you (Quadratic Functions) Thank you very much. You are truly a genius! |
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