ter Smitten's

The graph of the quadratic function is parabola.

• If , the parabola opens upwards. If , it opens downwards
• The vertex is
• The y-interacept =
• The x-intercepts are obtained by setting and solving for

This relationship between the value inside the square root (the discriminant), the type of solutions (two different solutions, one repeated solution, or no real solutions), and the number of x-intercepts (on the corresponding graph) of the quadratic is summarized in this table:

a positive number inside the square root	zero inside the square root	a negative number inside the square root
two real solutions	one (repeated) real solution	two complex solutions
two distinct x-intercepts	one (repeated) x-intercept	no x-intercepts

References:

• The Quadratic Formula Explained