Question

Help with question 14!!

Answer 1

Answer: a=2 b=5 c=-7

parabola equation is y = 2x^2+5x-7 = 0

Step-by-step explanation:

Substitute (x,y) into y = a x^2 + b x + c

(2,11)      11 = 4a + 2b + c

(-1,-10)  -10 = a - b + c

(-4,5)      5 = 16a -4b + c

Solve the linear system in a, b, c

Det[{{4,2,1},{1,-1,1},{16,-4,1}}] = 54

Det[{{11,2,1},{-10,-1,1},{5,-4,1}}] = 108

Det[{{4,11,1},{1,-10,1},{16,5,1}}] = 270

Det[{{4,2,11},{1,-1,-10},{16,-4,5}}] = -378

a = 108/54 = 2

b = 270/54 = 5

c = -378/54 = -7

parabola equation is y = f(x) = 2x^2+5x-7

f(2) = 8+10-7 = 11 ✔

f(-1) = 2-5-7 = -10 ✔

f(-4) = 32-20-7 = 5 ✔