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Math Help - How do you find the x-intercepts of Quadratic functions?

  1. #1
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    Question How do you find the x-intercepts of Quadratic functions?

    I've been Googling quadratic functions on how to to find the x-intercepts, I did find the instructions, but they're like "do this so this would equal this, etc" and they aren't really explaining how to do it... I have a test soon so I want to be able to know how to find the x-intercepts of quadratic functions in an easy way.

    One of my problems is f(x)= x^2 -7x+10
    Can someone tell me how to do these kinds of problems step by step?

    Another problem that is different from this is f(x)=x^2 -9x...
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  2. #2
    Senior Member slevvio's Avatar
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    Let's take a look at the equation you gave:

     f(x)= x^2 -7x+10

    To find the y-intercept you set x=0 in the equation and this will give you the y co-ordinate of the point where f(x) crosses the y-axis.

    so  f(0) = 10 i.e. f(x) crosses the y-axis at the point (0,10).

    To find the x-intercept you set f(x) = 0, i.e.

     x^2 -7x+10 = 0

    The easiest way to do this is to factorise:

     (x-2)(x-5) = 0
     \therefore x = 2 or x = 5
    (If factorising doesn't work use the quadratic formula x = \frac{-b \pm\sqrt{b^2-4ac}}{2a}.)

    So f(x) crosses the x-axis at the points (2,0) and (5,0).
    Last edited by slevvio; November 7th 2007 at 02:04 PM.
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