Respuesta :
Vertex form is a(x - b)^2 + c where the vertex is at (b, c)
here b = 0 and c = 3 and a = 1
so answer is D:- y = x^2 + 3
here b = 0 and c = 3 and a = 1
so answer is D:- y = x^2 + 3
Answer: The correct option is (D) [tex]y=x^2+3.[/tex]
Step-by-step explanation: We are given to select the correct equation that represents a parabola with vertex at the point (0, 3).
The standard equation of a parabola with vertex at (h, k) is given by
[tex]y=a(x-h)^2+k.[/tex]
Option (A) is
[tex]y= (x-3)^2.[/tex]
Comparing this equation with standard equation (i), we get
a = 1, vertex, (h, k) = (3, 0) ≠ (0, 3).
So, this option is not correct.
Option (B) is
[tex]y= (x+3)^2.[/tex]
Comparing this equation with standard equation (i), we get
a = 1, vertex, (h, k) = (-3, 0) ≠ (0, 3).
So, this option is not correct.
Option (C) is
[tex]y= x^2-3\\\\\Rightarrow y=(x-0)^3-3.[/tex]
Comparing this equation with standard equation (i), we get
a = 1, vertex, (h, k) = (0, -3) ≠ (0, 3).
So, this option is not correct.
Option (D) is
[tex]y= x^2+3\\\\\Rightarrow y=(x-0)^2+3.[/tex]
Comparing this equation with standard equation (i), we get
a = 1, vertex, (h, k) = (0, 3).
So, this option is correct.
Thus, (D) is the correct option.
