# Determine the x-and y-intercepts, the symmetry andthe vertex, and then draw the graph. of 4(x-2)^2

*print*Print*list*Cite

### 1 Answer

`y = 4(x-2)^2`

When y = 0 then we get the y intercept.

`0 = 4(x-2)^2`

`0 = (x-2)^2`

`0 = (x-2)`

`x = 2`

*So x intercept is 2.*

When x = 0 then we get the y intercept.

`y = 4(x-2)^2`

`y = 4(0-2)^2`

`y = 16`

**So y intercept is y = 16.**

For every value of x the value of `(x-2)^2>=0` . So the minimum of `(x-2)^2 = 0` and it comes when x = 2.

`y = 4(x-2)^2`

When x = 2 then y = 0. So minimum of y is 0 at x = 2. This is the vertex.

This is a quadratic function. Quadratic functions are symmetrical along its vertex. So ` y = 4(x-2)^2` is symmetrical along x = 2.

*The graph of the function is as follows.*