Question

a parabola contains the points (0,0),(-1,-2) and (1,6). what is the equation of the parabola in standard form?

Answer 1

Let the equation be:

y = ax^2 + bx + c.

Then, substitue the three points into the equation.

First point: 0 = a0^2 + b0 + c.

So  c = 0.

Second point: -2 = a(-1)^2 + b(-1) + c.

So  a - b + c = -2.

Third point: 6 = a*1^2 + b*1 + c.

So  a + b + c = 6.

We know that c=0 already, so we substitute c=0 into the last two equations and we would get:

a - b = -2

a + b = 6

We add the two equations and we get:

2a = 4

a = 2

Then, we substitute a=2 into a-b=-2 and we get:

-b = -4

b = 4

Now we know a = 2, b = 4, and c = 0

Then, the equation of the parabola would be:

2x^2 + 4x