Question

write a quadratic function in standard form with a leading coefficient (a value) of 2 that has the following real solutions- x=1/2 and x=-6

Answer 1

Use a(x - r1)(x - r2) with a = 2, r1 = 1/2, r2 = -6:

f(x) = 2(x - 1/2)(x + 6) = 2(x^2 + (11/2)x - 3) = 2x^2 + 11x - 6.