Find a, b, and c so that the parabola Y=ax^2+bx+c passes through the points (0,3), (1,0) and (-1,4)?

Question

Please show your work, thank you

Answer 1

(x,y)=(0,3) => x=0 & y=3 => 3=c (*)
(x,y)=(1,0) => x=1 & y=0 => 0=a+b+c (**)
(x,y)=(-1,4) => x=-1 & y=4 => 4=a-b+c (***)
Put c=3 in (**) &(***) then : a+b=-3 & a-b=1 => a=-1, b=-2 and you has y = -x^2-2x+3 the parabola. ok!!!

Answer 2

I'm not sure what your intention to get the answer but here's the answer for you. Hope this will help you resolve similar questions later.

First, plug 0 to x and 3 to Y.
Then, 3 = a (0)^2 + b(0) +c, this means that 3= 0 + 0 + c
So, c=3

Second, plug 1 to x and 0 to Y
Then, 0 = a (1)^2 + b + 3, this means that 0 = 2a + b +3

Third, plug -1 to x and 4 to Y
Then, 4 = a (-1)^2 + b (-1) + 3, this means that 4 = a -b+3
So, 1 = a - b, in other words, a = 1 + b

Finally, plug 1 + b to a in the second equation.
This means that 0 = 2 (1+b) + b + 3
Then, 0 = 2 + 2b+b+3 --> 0 = 5 + 3b
So, 3b= -5. This gives b = -5/3
plug the -5/3 to be in the third equation.
This means that a = 1 + (-5/3)
So, a = -2/3

Answer 3

(x=0,y=3): 3=a*0+b*0+c=c => c=3
(x=1,y=0): 0=a*1+b*1+c=a+b+3 => a+b=-3 (1)
(x=-1,y=4): 4=a*1-b*1+c=a-b+3 =>a-b=1 (2)
(1)+(2)=2*a=-3+1=-2 =>a=-1
a-b=1 => -1-b=1 =>b=-2
Parabola: y=-x^2-2x+3

Answer 4

This is a simple plug and chug problem.

You need to make three new equations, each by substituting (x,y) values into Y=ax^2+bx+c.

That will give you three linear equations in three variables (a,b,c), which you can then solve by simple algebra.

No fear! ACTION!!!

Answer 5

We substitute the coordinates
in the equation. We have
3=c..........1
0=a+b+c....2
4=a-b+c......3
from 1&2
a+b=-3
from 2&3&1
a+6=4
a=-2
b=-1
c=3

Answer 6

Plug each point (x,y) into the equation. Each will give you a different equation in a, b, c.

Now you have a neat three-equation, three-variable system to solve.