A quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (4, 3)(4,3). What is the vertex of the function defined as g(x)=f(-x)-5g(x)=f(−x)−5?

Answer 1

y = a(x-h)²+ k --> Vertex = (h,k)

y=a(x-4)²+3

Setting x to -x makes the parabola symmetric with the y-axis. Subtracting 5 moves the parabola down 5 units.

g(x) = f(x)-5 = a(-x-4)²+3-5 = a(-1)²(x+4)²-2 = a(x+4)-2

Which places the vertex of g(x) at (-4,-2).

The value of "a" stretches or shrinks the parabola, but doesn't change the vertex.