How would you describe how a quadratic function of y=ax2 +bx+c moves along the cartesian plane according to the parameter values of a,b and c.

Answer 1

y = ax^2 + bx + c

graphically has a y intercept = c or the point (0,c)

y= a(x^2 + (b/a)x + (b^2/4a^2)) + c - b^2/4a

y =a(x+ bx/2a)^2 + c -b^2/a in vertex form, with vertex = (-b/2a, c-b^2/4a)

axis of symmetry is x=-b/2a

use the quadratic formula

x = -b/2a + or - (1/2a)sqr(b^2 -4ac)

x intercepts are (-b/2a - sqr(b^2-4ac)/2a) and (-b/2a, sqr(b^2-4ac)/2a)

usually a "moving" y value is described using

h(t) = -(a/2)t^2 +vot + ho

where h(t)=y, ho=c, vo=b and -(a/2) =a, t=x

to compare it to y=ax^2 + bx^2 +c

then ho=c = initial height = initial y value= yo

vo = b = initial vertical velcoity at time t=0, = y'(o)

-a/2 = a = the effect of gravity's deceleration 32 ft/s^2 or 9.8 m/s^2

vertex = minimum point = minimum y or h value = minimum height, if a>0 or = maximum point= maximum y or h value if a<0

the graph of y(x) or h(t) is a parabola, upward opening if a>0, downward opening if a<0 for y=ax^2+bx +c or

upward opening if -a/2 <0, downward opening if -a/2>0 for h=-at^2/2 + vot + ho

y or h moves in the cartesian plane in a parabolic curve, with no global maximum or minimum. y or h approach infinity and negative infinity as x or t approaches infinity or negative infinity. Just one relative or local max or min.