Create the quadratic function that contains the points (0, -2), (1, 0) and (3, 10).

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

Step-by-step explanation:

We can write it in factor form as follows:

y =  a(x - 1)(x + c)

It's x - 1 because  1 is given as a root of the equation and a and c are constants.

Substituting the other given points:

-2 = a(0 - 1)(0 + c)

-ac = -2

ac = 2

Also:

10 = a(3 - 1)(3 + c)

10 = 2a(3 + c)

6a + 2ac = 10

But ac = 2, so:

6a + 4 = 10

6a = 6

a = 1.

ac = 2 so c = 2.

So our equation is  f(x) = (x - 1)(x + 2)

or f(x) = x^2 + x - 2.

answer

false

explanation

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