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 (- 4,3). This means that we have h=- 4 and k=3. We can use these values to partially write our function.
y=a(x-(- 4))^2+3
⇕
y=a(x+4)^2+3
We can see in the graph that the parabola opens upwards. Thus, a will be a positive 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 (- 8,7). Since this point is on the curve, it satisfies its equation. Hence, to find the value of a, we can substitute - 8 for x and 7 for y and simplify.
