What relationships can be found between the 'a', 'h', and 'k' points on a graph?

Answer 1

y= a(x-h)^2 + k is a quadratic equation, a vertical parabola with vertex = (h,k)

a is a stretching or compressing factor

or

x =a(y-k)^2 + h with comparble meanings for a,h and k

for horizontal parabola

or

the height formula with an object accelerating

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

a= acceleration of -32 feet per second per second

h = height at time t

v(t) = at + vo = 0 = h'(t)

t = vo/a = time for maximum height, vo= initial velocity, ho=initial height

max height = h(vo/a) = (a/2)(vo/a)^2 + vo(vo/a) + ho

= (vo^2)/2a + ho

maximum height in vertex form is (t,h) or (h,k) in the alternative (x,y) symobls

or often they'll use the metric system, then a= -9.8 meters per second per second