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 ( - 2,1). This means that we have h= - 2 and k=1. We can use these values to partially write our function.
y= a(x-( - 2))^2+1
⇕
y= a(x+2)^2+1
We can see in the graph that the parabola opens downwards. Therefore, a will be a negative number. To find its value, we will use the given point that is not the vertex.
We can see above that the point has coordinates (- 3,- 2). Since this point is on the curve, it satisfies its equation. Hence, to find the value of a, we can substitute - 3 for x and - 2 for y and simplify.
