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

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Answer 1 · 2017-12-09T21:25:30

As shown below:

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

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

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

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

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

Now we can find the intercepts:

$x = 0 \Rightarrow y = 4$ $x= 0 => y = 4$

Passes through $(0, 4)$ $(0,4)$

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

Passes thorugh $(\pm 2, 0)$ $(pm2,0)$ , these our roots.

How do you graph y=−x2+4y=-x^2+4?