Find the quadratic function that fits the data points (0,0) (3,0) and (5,2)


I dont want the answer, just need to know how to do it. An equation or something.

This page explains how to do it:

http://www.analyzemath.com/quadraticg/quadraticg.htm.

Find the quadratic function that fits the data points (0,0) (3,0) and (5,2).

right. first thing you need to know is that quadratics are in the form

y = ax^2 + bx + c

(0,0) is true. so substitute them into the equation

0 = a*0^2 + b*0 + c
0 = 0 + 0 + c
c = 0

as you can see, zeroes are pretty useful in this case

secondly, look at (3,0). substitute it in, knowing c = 0
0 = a*3^2 + b*3
9a + 3b = 0.............................(i)

there are two unknown variables here, so we would need to find another equation that is linearly independent (that is, not a multiple of the other)
fortunately, we know that (5,2) works so substitute that in

2 = a*5^2 + b*5
25a + 5b = 2 .................................(ii)

right, know solve via simultaneous equations.

i dunno, i think i may have done a mistake somewhere or i havent done this in ages, but im pretty sure this is the gist of it

What mantikore said, or if you're feeling ultra studly, use matrices to solve for the coefficients :P

Easy as fuck method: 0 and 3 are both zeros of the function. Thus, it is something like y=x*(x-3) [y=0 at x=0,3]. Now you just have to make it work for (5,2). 5*(5-3) = 10. Subtracting won't work because it'll throw off the values for x=0,3. So you divide by 5 instead.
y = x/5*(x-3) = 1/5*x^2-3/5*x

EDIT: If you want a general solution: Mantikore's right, but you should use all the zeros of the function before you solve the system of equations. Makes your life easier.

Thanks everyone for the replies, I failed the fuck out of the test anyways cause I didnt see the last few responses til today.

Im no good with math.

dont worry, with the level of maths im seeing in this thread, it looks like youre in the early stages of high school. youve still got time to learn everything.

i mean, i failed pretty much 70% of my maths tests at school (at one time getting only 10%), but for some reason, im doing engineering in university now, and the maths doesnt seem so hard

i think you will learn maths better if the stakes are high

That made me feel like shit.

I'm actually a freshman in college.

I took algebra in middle school, then geometry, algebra 2 and ap statistics in high school.

I didnt take any math my senior year, and basically fuckin forgot everything.

And im doing decent in the class, I just bombed that one test.