Answer:
Step-by-step explanation:
To determine the required fraction in vertex that can be represented by the graph with a vertex at (4,9) and through the point (2,5), we need to find the equation of the quadratic function that represents this graph.
The vertex form of a quadratic function is given by:
y = a(x - h)^2 + k
where (h, k) represents the vertex of the parabola. In this case, the vertex is (4,9), so we have:
y = a(x - 4)^2 + 9
Now, we can use the given point (2,5) to find the value of 'a'. We substitute the coordinates of the point into the equation:
5 = a(2 - 4)^2 + 9
Simplifying further:
5 = a(-2)^2 + 9
5 = 4a + 9
-4 = 4a
a = -1
Therefore, the equation of the quadratic function is:
y = -1(x - 4)^2 + 9
To express this as a fraction, we can write it as:
y = (-1/1)(x - 4)^2 + (9/1)
So, the required fraction in vertex that can be represented by the graph is -1/1.
