# How do you sketch the graph of #y=0.5(x-2)^2-2# and describe the transformation?

##### 1 Answer

- The y-intercept is at the origin,
#(0, 0)# . - The x-intercepts are

#(0,0)# and#(4,0)# . - The turning point is
#(2, -2)# .

graph{ y = 0.5(x-2)^2-2 [-10, 10, -5, 5]}

The graph has shifted 2 units to the right and 2 units down compared to

#### Explanation:

Since the equation is in the form of

Recall that:

- To find the y-intercept, let
#x-0# . - To find the x-intercepts, let
#y=0# , factorise the equation, and solve for#x# .

Let

The y-intercept is at the origin,

Let

Therefore, x-intercepts are

Now that you have all the information, let's graph it along with y=x^2.

graph{y=0.5(x-2)^2 - 2 [-10, 10, -5, 5]}

As you can see, the graph has shifted 2 units to the right and 2 units down compared to