Answer to Question #190894 in Algebra for Lovemore

Question

Finding variables a b and c in a parabola

Answer 1

The graph of a quadratic equation in two variables (y = ax² + bx + c ) is called a parabola. The following graphs are two typical parabolas their x-intercepts are marked by red dots, their y-intercepts are marked by a pink dot, and the vertex of each parabola is marked by a green dot:

We say that the first parabola opens upwards (is a U shape) and the second parabola opens downwards (is an upside down U shape). In order to graph a parabola we need to find its intercepts, vertex, and which way it opens.

 

 

Given y = ax² + bx + c , we have to go through the following steps to find the points and shape of any parabola:

1. Label a, b, and c.
2. Decide the direction of the paraola:
   
3. If a > 0 (positive) then the parabola opens upward.
4. If a < 0 (negative) then the parabola opens downward.