Respuesta :

Answer:

Step-by-step explanation:

The vertex form of a parabola is given by  y = a(x - h)^2 + k, where (h, k) is the vertex.

Given vertex at (2,-3), h = 2, k = -3

y = a(x - 2)^2 + (-3) = a(x - 2)^2 - 3

The parabola passes through (0,5) so

5 = a(0 - 2)^2 - 3

5 = 4a - 3

4a = 8

a = 2

The parabola equation in vertex form:

y = 2(x - 2)^2 - 3

Vertex form of parabola

  • y=a(x-h)^2+k

So

here

  • (h,k)=(2,-3)

Equation of parabola

  • y=a(x-2)^2-3

Now

  • Passes through (0,5)

[tex]\\ \rm\rightarrowtail 5=a(-2)^2-3[/tex]

[tex]\\ \rm\rightarrowtail 4a-3=5[/tex]

[tex]\\ \rm\rightarrowtail 4a=8[/tex]

[tex]\\ \rm\rightarrowtail a=2[/tex]

So

equation is

  • y=2(x-2)^2-3