The function g is defined as follows. g(x)=2x^2-5 If the graph of g is translated vertically upward by 3 units, it becomes the graph of a function h. Find the expression for h(x).

Explanation:

We shift the graph of g upward by 3 units. This means we add 3 onto g(x) like so

h(x) = g(x)+3

h(x) = (2x^2-5)+3

h(x) = 2x^2-5+3

h(x) = 2x^2-2

All points on g(x) move up by 3 units to get to a point on h(x). For instance, the y intercept (0,-5) on g(x) moves to (0,-2) on h(x).

When we say something like g(x)+3, we effectively mean y+3 to indicate an upward shift of 3 units. Recall that y = g(x) because they are both outputs.

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

hope this !

step-by-step explanation: