Identify the quadratic function that contains the points (-1,-4), (0,0) and (2,-10). f(x) = 3x^2 - x

f(x) = 3x^2+x

f(x) = - 3x^2+x

f(x) =-3x^2-x

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  (c)  f(x) = -3x^2 +x

Step-by-step explanation:

Points either side of (0, 0) have lower y-values, so you know the parabola opens downward. This eliminates the first two choices.

Trying one of the other points in the one of the remaining equations tells you which equation works.

For example, usint (-1, -4) in the third choice, we get ...

  f(-1) = -3(-1)^2 +(-1) = -3 -1 = -4 . . . . . matches point (-1, -4)

The correct function is the third choice:

  f(x) = -3x^2 +x

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: