The vertex form of a quadratic equation is expressed as
y = a(x - h)^2 + k
where
h and k are the x and y x and y coordinates of the vertex of the parabola.
a is the leading coefficent
From the information on the graph,
h = 13
k = 13
By substituting these values into the formula,
y = a(x - 13)^2 + 13
On the graph, when x = 26, y = 0
Substituting these values into the equation, we have
0 = a(26 - 13)^2 + 13
0 = a * 13^2 + 13
0 = 169a + 13
169a = - 13
a = - 13/169
a = - 1/13
By substituting a = - 1/13, h = 13 and k = 13 into the verte form equation, the quadratic equation written in vertex form is
y = - 1/13(x - 13)^2 + 13