What kind of transformation converts the graph of f(x)=–10(x+5)2+4 into the graph of g(x)=–10(x+7)2+3?

The transformation that converts the graph of f(x)=-10(x+5)²+4 into the graph of g(x)=-10(x+7)²+3 is a horizontal shift to the right by 2 units and a vertical shift down by 1 unit.

Here's the step-by-step explanation:

1. The general form of a quadratic function is f(x)=a(x-h)²+k, where (h,k) is the vertex of the parabola. In this case, for f(x), h=-5 and k=4, and for g(x), h=-7 and k=3.

2. The change in the h-value from -5 to -7 represents a shift to the right by 2 units. This is because the sign in front of the h-value is opposite to the direction of the shift. So, a change from -5 to -7 means a shift to the right by 2 units.

3. The change in the k-value from 4 to 3 represents a shift down by 1 unit. This is because the k-value represents the vertical shift, and a decrease in the k-value means a shift downwards.

So, the transformation that converts the graph of f(x) into the graph of g(x) is a horizontal shift to the right by 2 units and a vertical shift down by 1 unit.