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

May 12, 2018

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

#### Explanation:

Change the equation to vertex form ($y = a {\left(x - h\right)}^{2} + k$) for easier comprehension.
$f \left(x\right) = - {\left(x - 1\right)}^{2} + 4$

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 $\left(1 , 4\right)$.

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
.
$0 = - {\left(x - 1\right)}^{2} + 4$

$4 = {\left(x - 1\right)}^{2}$

$\pm 2 = x - 1$

${x}_{1} = 2 + 1 , {x}_{2} = - 2 + 1$

${x}_{1} = 3 , {x}_{2} = - 1$

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