graph the function f(x)=-(x-2)^2+4

Question

It said Graph the function  

Answer 1

You should know that the graph of y = x² is a parabola.

 

The negative in front flips it upside down, the -2 moves it 2 to the right, and the +4 moves it up 4. You should have an upside down parabola with a vertex of (2,4). You may want to input other x-values to find other points.

 

f(1) = -(1 - 2)² + 4 = -(-1)² + 4 = -1 + 4 = 3, so (1,3) is a point on your parabola.

Answer 2

"It said" graph the function.

You can do so by making a table of x,y values.Better yet, you can begin by analyzing a series of simple transformation on the basic graph of y = x^2.

 

1.  shift the basic parabola two units to the right

2.  reflect this over the x-axis (i.e. changing all y values to their opposites--parabola now has vertex at (2,0) and is upside down

3.  shift all points up FOUR units.