Random Notes on Quadratics


1. We set ax2 + bx + c = 0

So we are saying what is the value of x when y is 0

2. If the discriminant SQRT(b2 - 4ac) = 0 then x will only have one value (when y is 0)

3. If the discriminant is negative, there are no solutions for y = 0 (which is why we have square root of a negative number - it never hits y line)

4. If the discriminant is > 0 then we have 2 x values for y = 0

5. for ax˛ + bx + c
if a > 0 (parabola opens up
if a < 0 (parabola opens down)

6. -b/2a is the x value of the vertex because it is the x value of the minimum or maximum point. It is the value of x when the discriminant is 0. It will be the only place where x has only 1 value. In all other spots x will have a greater (and a smaller) value and the parabola grows.