Chapter 2 - Nonlinear Functions - 2.2 Quadratic Functions; Translation and Reflection - 2.2 Exercises - Page 64: 11

$(2, -1)$

$ f(x)=a(x-h)^{2}+k^{2},\qquad$ vertex: (h,k) (solved as in example 4) $(A\pm B)^{2}=A^{2}\pm 2AB+B^{2}$ ----------- $y=-2x^{2}+8x-9$ $=-2(x^{2}-4x)-9$ $=-2(x^{2}-2\cdot 2\cdot x+4-4)-9$ $=-2(x^{2}-4x+4)-9-(-2)(4)$ $=-2(x-2)^{2}-1$ Vertex: $(2, -1)$.