1. ## Modeling With Quadratic Equations

Okay, well I need a little help understanding this.

Apparently from my homework I am given a parabola with 3 points, (0,0),(2,-2), and (3,4). I just need help understanding how to figure out the equation in standard form (y=ax^2+bx+c).

So far all I have is:

-2=a(1)^2+b(1)+c -> -2 = a+b+c
-2=a(2)^2+b(2)+c -> -2 = 4a+2b+c
4=a(3)^2+b(3)+c -> 4 =9a+3b+c

All I really have to do is figure out what a,b, and c are and I can figure out the rest.

Also, can you help explain how you came across doing it?

Thanks

2. Originally Posted by JosephLive93
Okay, well I need a little help understanding this.

Apparently from my homework I am given a parabola with 3 points, (0,0),(2,-2), and (3,4). I just need help understanding how to figure out the equation in standard form (y=ax^2+bx+c).

The 3 given points are your 3 clues to find the 3 values a, b, c.

So far all I have is:

-2=a(1)^2+b(1)+c -> -2 = a+b+c........you need f(0)=0 here, or should that point have read (1,-2) ?
-2=a(2)^2+b(2)+c -> -2 = 4a+2b+c
4=a(3)^2+b(3)+c -> 4 =9a+3b+c

All I really have to do is figure out what a,b, and c are and I can figure out the rest.

Also, can you help explain how you came across doing it?

Thanks
$f(0)=0\Rightarrow\ a(0)+b(0)+c=0\Rightarrow\ c=0$

$f(2)=-2\Rightarrow\ a(2)^2+b(2)=-2$

$f(3)=4\Rightarrow\ a(3)^2+b(3)=4$

With $c$ accounted for, you only need solve the remaining pair of simultaneous equations
for $a$ and $b.$