How do you graph y = -x^2 + 3?

1 Answer
Jun 13, 2015

graph{-x^2+3 [-10, 10, -5, 5]}

Explanation:

The equation is of the kind

y=ax^2+bx+c a=-1, b=0, c=3 which means it is a parabola whose axis is parallel to the y axis. Notice that a<0 so it is a downward facing parabola.

Now you have to calculate the vertex:

use the formula
2ax_v+b=0 => x_v=-b/2a => x_v=0
y_v=ax_v^2+bx_v+c=0+0+3=3

So the vertex is in (0,3), the axis is parallel to the y axis and intersect the curve in (0,3) => it's the y axis => the parabola is symmetric on the y axis.

Then you calculate the intersection with the x axis. Trivially, they are (sqrt(3),0) and (-sqrt(3),0)

Now use what you know and draw the curve, as in the graph.