The possible functions are
A. F(x)=2x^2-8x-42
B. F(x)=5x^2+20x-105
C. F(x)=x^2+4x-21
How to determine the possible equations?
The zeros are given as:
x = -7 and x = 3
Rewrite as:
x +7 = 0 and x - 3 = 0
Multiply both zeros
(x + 7) * (x - 3) = 0 * 0
Evaluate the product
x^2 + 7x - 3x - 21 = 0
Evaluate the like terms
x^2 + 4x - 21 = 0
Express as a function
f(x) = a(x^2 + 4x - 21)
Where a is a constant
Let a = 1, 2 and 5 (according to the values in the options)
f(x) = 1 * (x^2 + 4x - 21) = x^2 + 4x - 21 --- option (c)
f(x) = 2 * (x^2 + 4x - 21) = 2x^2 + 8x - 42 --- option (a)
f(x) = 5 * (x^2 + 4x - 21) = 5x^2 + 20x - 105 --- option (b)
Hence, the possible functions are (a), (b) and (c)
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