Question

Identify the vertex and the y intercept of the graph of the function y=0.5(x-3)^2

Answer 1

y = 0.5(x - 3)^2
This is a parabola (2nd power).
The vertex is (3,0).
The y intercept will be 4.5
If you put zero in for x, (because it is on the y-axis), the value will be 4.5.

Answer 2

The vertex of the function is (3,0).

The y-intercept is (0,4.5).

Explanation:

Given : Function
`y=0.5(x-3)^2`

To find : Identify the vertex and the y intercept of the graph of the function?

Solution :

The given function is a equation of a parabola.

The equation of a parabola in vertex form is
`y = a(x - h)^2+ k`

where (h, k) are the coordinates of the vertex and a is a multiplier

On comparing with given equation,

h = 3 and k = 0,

So, The vertex of the function is (h,k) = (3,0)

To find the y- intercept,

Put x = 0 in the function,

`y=0.5(0-3)^2`

`y=0.5* 9`

`y=4.5`

So, The y-intercept is (0,4.5).