The parent function f (x) = x2 is reflected across the x-axis, vertically stretched by a factor of 4, and translated right 3 units to create g (x). Use the description to write the quadratic function in vertex form.
g (x) = 4(x + 3)2
g (x) = 4(x - 3)2
g (x) = -4(x - 3)2
g (x) = -4 (x + 3)2

Two line segments are shown in the figure below. suppose that the length of the line along the x-axis is 6, and the length of the hypotenuse of the triangle is 10. what is the equation of the hypotenuse line (shown in red, below)?

Ms.ortiz sells tomatoes wholesale. the function p(x)=-80x^2+320x-10, graphed below, indicates how much profit she makes on a load of tomatoes if she makes on a load of tomatoes if she sells them for 4-x dollars per kilogram. what should ms.ortiz charge per kilogram of tomatoes to make on a load of tomatoes?

Amachine part consists of a half sphere and a cylinder, as shown in the figure. the total volume of the part is π cubic inches.