Question

1) The quadratic function f(x) has a vertex at (5,-8). If g(x)=f(x+7)-3,

then at which of the following does g(x) have a vertex?

Answer 1

The vertex of the quadratic function g(x) will be at (-2, -11), after applying the given transformations to the original function f(x) with the vertex at (5, -8).

Step-by-step explanation:

The student is asking about the vertex of a transformed quadratic function. The original function, f(x), has a vertex at (5, -8). The transformed function, g(x) = f(x + 7) - 3, will have its vertex shifted to the left by 7 units along the x-axis and down by 3 units along the y-axis, due to the transformations applied. Hence, the vertex of g(x) will be at (5 - 7, -8 - 3), which simplifies to (-2, -11).