We want to write the equation of the given parabola. To do so, let's recall the vertex form of a quadratic function.
y= a(x- h)^2+ k
In this expression, a, h, and k are either positive or negative constants. Let's start by identifying the vertex.
The vertex of this parabola has coordinates ( 0, 2). This means that we have h= 0 and k= 2. We can use these values to partially write our function.
y= a(x-( 0))^2+ 2
⇕
y= ax^2+2
We can see in the graph that the parabola opens downwards. Thus, a will be a negative number. To find its value, we will use a point that lies on the parabola. Let's choose the point (1,- 1).
Since this point is on the curve, it satisfies its equation. Hence, to find the value of a, we can substitute 1 for x and -1 for y and simplify.
