Answer: a = 2 b = 3 c = 5
Literally a+ b+c = 10, but I don't think that's what the question means to ask.
the equation is 2x² +3x + 5
Step-by-step explanation: Substitute the values of the given coordinates into the formula and use algebra (solve a system of equations by substitution and elimination) to get the values of a,b & c
y=ax²+bx+c using (0,5), (1,10), and (2,19)
5=a(0)²+b(0)+c becomes 5= 0+0 + c .so we find c = 5
10=a(1)²+b(1)+c becomes 10 = a + b + c
19=a(2)²+b(2)+c . becomes 19 = 4a + 2b + c
Substitute the 5 for c. Then rewrite
10 = a + b + 5 becomes 5 = a+ b to eliminate b multiply this be (-2)
(-2)( 5 = a+ b) .to get -10 = -2a - 2b
19 = 4a + 2b + 5 becomes 14 = 4a + 2b
_______________ Add these two
14 = 4a + 2b
-10 = -2a - 2b this will eliminate the "b" term
4 = 2a divide both sides by 2 so you have a = 2
substitute in 10=a(1)²+b(1)+5 to find b
10=2(1)²+b(1)+5 .becomes 5 = 2 + b Subtract 2 from both sides
b = 3
So now you have all three values:
a = 2 b= 3 c = 5
I am attaching the graph. I hope this deserves Brainiest.
Best wishes in your studies!
