A parabola opening up or down has vertex ( – 6,5) and passes through (– 20, – 29/4). Write its equation in vertex form.

Answer 1

y = a(x+6)^2 + 5

-29/4 = a(-20+6)^2 + 5

-29/4 = 196a +5

a = (-29/4 -20/4)/196 = (-49/4)/196 = -1/16

y = (-1/16)(x+6)^2 + 5 is the equation of the downward opening parabola in vertex form

-29/4 = (-1/16)(-20+6)^2 + 5

= -(1/16)(-14)^2 +5

= -(196)/16 +5

= -49/4 +5

= -49/4 +20/4

= (-49+20)/4

= -29/4