if the graph of a quadratic fuction passes through the points (-1,0) (-2,0) and (0,2), what is the general form

Question

What is the general form of a quadratic function that passes through (-1,0) (-2,0) and (2,0)

Answer 1

You have 3 points and need to find ax² + bx + c = y. First use (0,2). x is zero, so y = 2 = c. You have c. Now put (-1,0) into the equation. 0 = 1a -b + 2. Rearrange so you get b = a + 2. Now use the other point. a*(-2 squared) + b*(-2) + 2 = 0. Simplify and substitute (a + 2) for b and you will have the answer.