How do the points where the graph cuts the x axis relate to the axis of symmetry of the graph and the solutions of the quadratic equation ax^2 + bx + c = 0?
Match the graphs in the diagram to the following descriptions and give reasons for your decisions.
- y = ax^2 + bx + c if a > 0, b > 0 and c < 0.
- y = ax^2 + bx + c if a < 0, b = 0 and c > 0.
- y = ax^2 + bx + c if a < 0, b < 0 and b^2 - 4ac < 0.
- y = a(x+p)^2+q if p < 0, q < 0 and the x-intercepts have different signs.
- y = a(x+p)^2+q if a < 0, p < 0, q > 0 and one root is zero.