Question

a parabola contains the point (1,-2),(2,-2), and (3,-4). what is the equation of this parabola in standard form?

Answer 1

The most appropriate equation of a parabola to use in solving this particular problem is y=ax^2 + bx + c, where a, b and c are the constant coefficients whose values we must find.

Thus, we'll need three equations in three unknowns {a, b, c} to determine {a, b, c}.

Starting with the given point (1,-2): we see that x=1 and y=-2. Substitute these into y=ax^2 + bx + c: -2=a(1)^2 + b(1) + c.
Do the same thing for the other two points, (2,-2) and (3,-4).

I ended up with the following system:
a+b+c=-2
4a+2b+c=-2
9a+3b+c=-4

This system could be solved in a variety of ways. I used the matrix tools on my TI-84 calculator. Other methods of solution include addition/subtraction, substitution, determinants, and so on.

Good luck!

Once you have the values of {a, b, c}, simply substitute them into y=ax^2 + bx + c to arrive at the equation of the parabola in standard form.