Quadratic Functions, Parabolas, or Polynomials of Order 2
The function
y = ax2 + bx +c
is the general quadratic or polynomial of the second degree. We graph
y = ax2 + 2x - 2
for a from +1 down to -1.
The parabola opens up, or is concave up, when a is positive and opens
down, or is concave down, when a is negative. Watch how the location of the vertex changes.
Could you find a function describing the coordinates of the vertex?
The function
y = 0.5 x2 + bx - 2
is graphed below for b from -4 to +4.
Can you describe the curve that the vertex follows as b changes? Is it
possibly another parabola?