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 $(3,0)$ .

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