Step-by-step explanation:
The vertex of a parabola is either the minimum or maximum value of it, depending on which way the parabola is facing. It is where the axis of symmetry passes through.
The vertex form of a quadratic equation is given by the following:
f(x) = a(x-h)^2 + k
Here, the h value is the movement of the parabola shift horizontally
k is the value of the shift vertically
Together, we have the point for the vertex, (3,5)
a is the stretch or compression of the graph
These are the 3 values we need to form a quadratic equation (h, k, and a)
Since we are given the vertex and the point at which x is equal to 0 (y-intercept,) we can calculate what this parabola looks like.
We can plug in our values to the equation above to calculate a.
1 = a(0-3)^2 + 5
1 = a(0-3)(0-3)^2 + 5
1 = a(9) + 5
-4 = 9a
a = [tex]-\frac{4}{9}[/tex]
Now that we have the a value, we have an equation to use:
[tex]f(x) = -\frac{4}{9} (x-3)^2 + 5[/tex]
Not sure how to make a graph on here but I assure you that plugging that into a graphing calculator will give you the graph you need, and using this method and understanding will allow you to solve it on your own now.
