Triangles RST and LMN are similar. Triangle RST has lengths 4.1 millimeters, 3.9 millimeters, and 6.3 millimeters. Triangle LMN has lengths 2.46 millimeters, 2.34 millimeters, and 3.78 millimeters, respectively. What is the constant of proportionality from RST and LMN?

a = 4, b = - 8, c = - 60

Step-by-step explanation:

If the graph passes through these points, these points must satisfy the equation of the locus of that function, for each x and y.

For the solution (5, 0),

f(x) = y = ax^2 + bx + c

for (x, y) = (5, 0)

=> 0 = a(5)^2 + b(5) + c

=> 0 = 25a + 5b + c ...(1)

For (x, y) = (-3, 0)

=> 0 = a(-3)^2 + b(-3) + c

=> 0 = 9a - 3b + c ...(2)

For (x, y) = (-5, 80)

=> 80 = a(-5)^2 + b(-5) + c

=> 80 = 25a - 5b + c ...(3)

Subtract (1) from (3) we get,-80 = 10b => -8 = b. Thus, eq(1) is 40 = 25a + c, eq(2) is - 24 = 9a + c

Subtract (1) from (2),

64 = 16a => 4 = a

Hence, in eq(1), 40 = 25(4) + c, - 60 = c