Can someone explain to me how to write an equation (doesn't matter what form) of a parabola that passes through the points (-5,-4), (-4,0) and (0,1)? : )

Ok so

parabola is a quadratic equation

(x,y)
this is fun

ok so
y=ax^2+bx+c
now sub the three points into three equations like that

remember (x,y)
so we have
-4=a(-5)^2+b(-5)+c
0=a(-4)^2+b(-4)+c
1=a(0)^2+b(0)+c

simplified
-4=25a-5b+c
0=16a-4b+c
1=c
nice, we know that c=1
now sub 1 for every c

-4=25a-5b+1
0=16a-4b+1
now minus 1 from both sides of all equations
-5=25a-5b
-1=16a-4b
simplify first equation by dividing everybody by 5
-1=5a-b

we have
-1=5a-b
-1=16a-4b
try to eliminate a or b
eliminate b
multiply first equation by -4 and add to second

-1=16a-4b
4=-20a+4b +
3=-4a+0b

3=-4a
divide both sides by -4
-3/4=a
sub back to find b
-1=5a-b
-1=5(-3/4)-b
-1=-15/4-b
-1=-3 and 3/4-b
add 3 and 3/4 to both sides
2 and 3/4=-b
times both sides by -1
-2 and 3/4=b
-11/4=b
a=-3/4
b=-11/4
c=1

the equation is
y=-3/4x^2-11/4x+1

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