1. ## 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...

2. Let's take a look at the equation you gave:

$\displaystyle f(x)= x^2 -7x+10$

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

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

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

$\displaystyle x^2 -7x+10 = 0$

The easiest way to do this is to factorise:

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

So $\displaystyle f(x)$ crosses the x-axis at the points (2,0) and (5,0).