How do you graph y=-x^2+4?

Dec 9, 2017

As shown below:

Explanation:

The first thing to do is identify what tranformations ${x}^{2}$ should undergo to reach $- {x}^{2} + 4$

$- {x}^{2} + 4$ is just ${x}^{2}$ reflected in the x axis, then translated by $\left(0 , 4\right)$ or in words, shifted upward by 4 units

${x}^{2}$:
graph{x^2 [-9.625, 10.375, -2.96, 7.04]}

$- {x}^{2}$ : graph{-x^2 [-9.42, 10.58, -8, 2]}

$- {x}^{2} + 4$:
graph{4- x^2 [-9.375, 10.625, -4.32, 5.68]}

Now we can find the intercepts:

$x = 0 \implies y = 4$

Passes through $\left(0 , 4\right)$

$y = 0 \implies {x}^{2} = 4 \implies x = \pm 2$

Passes thorugh $\left(\pm 2 , 0\right)$, these our roots.