Answer:
[tex]\large \boxed{-4}[/tex]
Step-by-step explanation:
The vertex form of the equation for a parabola is
y = a(x - h)² + k
where h and k are the coordinates of the vertex
and a is the coefficient of x² in the standard form.
Data:
Vertex at (3,11)
A point at (2,7)
Calculations:
1. Substitute the coordinates of the vertex into the equation
y = a(x - 3)² + 11
2. Substitute the coordinates of the point into the equation and solve for a
[tex]\begin{array}{rcl}7 & = & a(2 - 3)^{2} + 11\\7 & = & a(-1)^{2} + 11\\7& = &a + 11\\a & = & \mathbf{-4}\\\end{array}\\\text{The coefficient of x$^{2}$ in the parabola's equation is $\large \boxed{\mathbf{-4}}$}[/tex]
