How do you graph #f(x) = 4 - (x-1)^2#?

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Answer 1 · 2018-05-12T06:13:30

graph{y=4-(x-1)^2 [-10, 10, -5, 5]}

Change the equation to vertex form (#y=a(x-h)^2+k#) for easier comprehension.
#f(x)=-(x-1)^2+4#

We know that the vertex of a parabola is always at #h# and #k# of its equation in vertex form. So, we can plot its vertex at #(1,4)#.

Additionally, since the #a# value is #-1#, we know the parabola will open downward.

Then, solve for the roots (zeros) using the equation by making the equation equal to 0
.
#0=-(x-1)^2+4#

#4=(x-1)^2#

#+-2=x-1#

#x_1=2+1, x_2=-2+1#

#x_1=3,x_2=-1#

Now the calculations are over, graph a parabola opening downward with its vertex at #(1,4)# going through #(-1,0)# and #(3,0)#.