Answer
Vertex: (0,0)
Axis of Symmetry: x=0
graph opens upward
Work Step by Step
To find the Vertex of the equation H(x)= 2x^2, you must find your A, B, and C values. The A=2. And since we don't have a B or C value, they both equal 0.
To find the x value of the vertex, use the formula x= -B/2A. so...
x= -0/2(2)
x= 0/4
x= 0
Now plug the x you just found into the equation for the x value.
h(0)= 2(0)^2
h(0)= 0^2
h(0)= 0
so the vertex is (0,0)
To find the axis of symmetry you also use x= -B/2A
x= -0/2(2)
x= 0/4
x=0
so the axis of symmetry is x=0.
In order to graph the equation, we must find two more points. Any number can be plugged into the equation, but I'm going to use 1 and -1. So..
2\times(1)^2= h(1)
2\times1= h(1)
2= (h1)
so (1, 2) will be a point on the graph.
2\times(-1)^2= h(-1)
2\times1= h(-1)
2= h(-1)
so (-1, 2) will be the last point on the graph.
The graph will open upward because the A value of the equation is greater than 0
