+386 We have a curve y=ax^2 +bx +c
coords : (1,2) , (-2,5) and (0,-2) all are part of the function
Find it's equation (find a, b and c)
The answer is y= 5/2 (x^2) + 3/2 (x) -2 , so a=5/2 b=3/2 and c=-2
I need the complete steps, cause I keep doing something wrong along the way and I cannot point out what it is.
Here's what I'm pretty sure is ok, go from there:
(0,-2):
-2=a(0)^2+(0)b +c
-2=c
(1,2):
2=a(1)^2 + (1)b -2 (replacing c with -2 from now on)
2=a+b-2
4=a+b
(-2,5):
5=a(-2)^2+b(-2)-2
5=4a-2b-2
7=4a-2b
System of equations:
L1: 4=a+b
L2: 7=4a-2b
+259 Well I just tried to solve what u given my way. U actually did everything right, so I dont really know how I can help u, but as u asked for a complete solve I just tried it myself. Well u can prob. skip half of that part tbh.
y = ax^2 + bx + c
(1, 2)
2 = a + b + c
(-2, 5)
5 = 4a - 2b + c
(0, -2)
-2 = c
Now lining up all letters:
1a + 1b + 1c = 2
4a - 2b + 1c = 5
c = -2
So now to solve this equation just put the 3rd equation into the 2nd and first. (Well till now just repeating what u have done.)
I just try to hold on to c till the equation as it makes things look more easier and clear.
1a + 1b - 2 = 2 II * 2.5
4a - 2b - 2 = 5
2.5a + 2.5b - 5 = 5
4a - 2b - 2 = 5
now im trying to solve this equation by isolating a or b, as is already given. (in this case im isolating a)
2.5a + 2.5b - 5 = 4a - 2b -2 II + 2 II +2b II - 2.5a
4.5b - 3 = 1.5a II /1.5
3b - 2 = a
putting a into the first or second equation. (in this case the first)
3b - 2 + 1b - 2 = 2 II +4
4b = 6 II /4
b = 1.5
Now u can put b into ur a equation :
3*1.5 - 2 = a
4.5 - 2= a
2.5 = a
I hope i didnt do any mistake. But it should be a = 2.5, b= 1.5 and c= -2. (As u said in the question)
So y = ax^2 + bx + c
y = 2.5x^2 + 1.5x - 2
