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

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• Nov 7th 2007, 02:25 PM
clay10
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...
• Nov 7th 2007, 02:53 PM
slevvio
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).