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 ( -3,6). This means that we have h= -3 and k=6. We can use these values to partially write our function.
y= a(x-( -3))^2+6
⇕
y= a(x+3)^2+6
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 the given point that is not the vertex.
We can see above that the point has coordinates (-5,2). Since this point is on the curve, it satisfies its equation. Hence, to find the value of a, we can substitute -5 for x and 2 for y and simplify.
