If the vertex of a parabola is (3,11) and another point on the curve is (2,7),what is the coefficient of the squared expression in the parabola's equation?

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]