Question

Which of the following equations is of a parabola with a vertex at (0, 3)?

y = (x - 3)2
y = (x + 3)2
y = x2 - 3
y = x2 + 3

Answer 1

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

Answer 2

Answer: The correct option is (D)
`y=x^2+3.`

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

`y=a(x-h)^2+k.`

Option (A) is

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

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

`y= (x+3)^2.`

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

`y= x^2-3\\\\\Rightarrow y=(x-0)^3-3.`

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

`y= x^2+3\\\\\Rightarrow y=(x-0)^2+3.`

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.