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,- 4). This means that we have h=3 and k=- 4. We can use these values to partially write our function.
y=a(x-3)^2+(- 4)
⇕
y=a(x-3)^2-4
We can see in the graph that the parabola opens upwards. Therefore, 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 (5,4). 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 4 for y and simplify.
