Question

Write an equation of the parabola in vertex form that passes through ( 3 , -2 ) and has a vertex of ( 5,8 )

Answer 1

Hi,

Explanation:

Parabola has the equation:

y=k*(x-5)²+8

if x=3, y=-2: -2=k*(-2)²+8 ==> 4k=-10==> k=-5/2

So y=-5/2(x-5)²+8

Answer 2

Parabola in vertex form: y = a(x - h)2 + k

Vertex: (h, k) = (3, 2) and (x, y) = (13, 8)

y = a(x - h)2 + k

y = a(x - 3)2 + 2 <== with substitution (h, k) = (3, 2)

8 = a(13 - 3)2 + 2 <== with substitution (x, y) = (13, 8)

8 = a(10)2 + 2

100a = 8 - 2 ==> 100a = 6 ==> a = 6/100 ==> a = 3/50

Parabola in vertex form: y = a(x - h)2 + k

y = (3/50)(x - 3)2 + 2 (Final Answer - Parabola in vertex form)

Explanation: