SOLUTION: Sketch the graph of f(x) = (x-6)^2 + 2. Label all x-intercept, y-intercepts and the vertex.

Question 128196: Sketch the graph of f(x) = (x-6)^2 + 2. Label all x-intercept, y-intercepts
and the vertex.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given function

To find the x-intercepts, simply let

Plug in

Subtract 2 from both sides

Take the square root of both sides.

Since you cannot take the square root of a negative number, there are no real x-intercepts. So this means that the graph does not cross the x-axis. So there are no x-intercepts.

Now to find the y-intercepts, simply plug in

Start with the given function

Plug in

Subtract

Square -6 to get 36

Add

So when , . So the y-intercept is (0,38)

Now because is in vertex form where (h,k) is the vertex, we can see that the vertex is (6,2)

So putting all of this together, we get

Graph of

and we can see that there are no x-intercepts, the graph has a y-intercept (0,38), and the vertex is (6,2). So this visually verifies our answer.
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