Question

How do you graph the parabola `y= - 1/2 * x^2` using vertex, intercepts and additional points?

Answer 1

I hope this help.

Explanation:

Using Vertex
Y=`-1/2*x^2`

Y=`-x^2/2`

Use the Vertex Form is y=`a(x-h)^2+k`
a=`-1/2`

h= 0
k=0
{(0,0)
Vertex graph{y=-1/2x^2 [-10, 10, -5, 5]}

Intercept
Find P the distance from Vertex to the focus
`-1/2`
Find focus (h,k+p)
(0, `-1/2`)
x=0

y=`1/2` (this answer get from subtract p from the y-coordinate k of the vertex if the parabola opens up or down "y=k-p")
Vertex (0,0)
Focus: (0,`-1/2`)
Axis of Symmetry: x=0
Directrix: y=`1/2`