First we will first express the equation in standard form, y=a(x-h)^2+k, where a, h, and k are either positive or negative constants.
y=- 1/2x^2
⇕
y=- 1/2(x-0 )^2+0It is important to note that we do not need to graph the parabola to identify the desired information. Let's compare the general formula for the standard form to our equation.
General Formula:y=& a(x- h )^2 +k
Equation:y=& - 1/2(x- 0)^2+
We can see that a= - 12, h= 0, and k= .
Vertex
The vertex of a quadratic function written in standard form is the point ( h,k). For this exercise, we have h= 0 and k= . Therefore, the vertex of the given equation is ( 0, ).
Axis of Symmetry
The axis of symmetry of a quadratic function written in standard form is the vertical line with equation x= h. As we have already noticed, for our function, this is h= 0. Thus, the axis of symmetry is the line x= 0.
Direction of Opening
Recall that, if a>0, the parabola opens upwards. Conversely, if a<0, the parabola opens downwards.
In the given function, we have a= - 12, which is less than 0. Thus, the parabola opens downwards.
