Math basics › Quadratics and polynomials
Parabolas
Which way it opens
a > 0 opens up and has a lowest point. a < 0 opens down and has a highest point.
The vertex
x = −b/2a, then put that x back in to get y. The axis of symmetry is the vertical line through it.
Vertex form
y = a(x − h)² + k puts the vertex at (h, k). Note the minus sign: (x − 3)² moves it right, not left.
Roots are where it crosses
The solutions of ax² + bx + c = 0 are the x-intercepts. Two answers means two crossings.