I have two questions, please help.

1. Determine the quadratic function f whose vertex is (2,-1) and passes through (1,1).
f(x)=?
type in form f(x)=ax^2+bx+c
**pleasae show work**

2. Describe for the graph of g(x)=3square root x+2 can be obtained from the graph of f(x)=3square root x
a. shift graph 2 units right
b. shift graph 2 units down
c. shift graph 2 units up
d. shift graph 2 units left

over look please

(y+1) = k (x-2)^2

2 = k(1)
k = 2
so
(y+1) = 2(x-2)^2
y+1 = 2(x^2 -4 x + 4) = 2 x^2 -8 x + 8

y = 2 x^2 - 8 x + 7

Sure! I can help you with both questions.

1. To determine the quadratic function f whose vertex is (2,-1) and passes through (1,1), we can use the vertex form of a quadratic function, which is given by f(x) = a(x-h)^2 + k, where (h,k) represents the vertex of the parabola.

We are given that the vertex is (2,-1). So, we have h = 2 and k = -1. Substituting these values into the vertex form, we get f(x) = a(x-2)^2 - 1.

Now, to find the value of "a," we can use the fact that the function passes through the point (1,1). Substituting x = 1 and f(x) = 1 in the equation f(x) = a(x-2)^2 - 1, we get 1 = a(1-2)^2 - 1.

Simplifying this equation, we have 1 = a(-1)^2 - 1, which becomes 1 = a - 1.

This implies a = 1 + 1, which gives us a = 2.

Now we have determined the value of "a," so the quadratic function f(x) is f(x) = 2(x-2)^2 - 1.

Therefore, the answer is:
f(x) = 2x^2 - 8x + 7.

2. The graph of g(x) = 3√(x) + 2 is obtained from the graph of f(x) = 3√(x) by applying vertical (up/down) and horizontal (left/right) shifts.

a. To shift the graph 2 units right, we replace x with (x - 2) in the function g(x). So, g(x) = 3√(x - 2) + 2.

b. To shift the graph 2 units down, we subtract 2 from the function f(x). So, g(x) = 3√(x) + 2 - 2 = 3√(x).

c. To shift the graph 2 units up, we add 2 to the function f(x). So, g(x) = 3√(x) + 2 + 2 = 3√(x) + 4.

d. To shift the graph 2 units left, we replace x with (x + 2) in the function g(x). So, g(x) = 3√(x + 2) + 2.

Therefore, the correct answer is (c) shift the graph 2 units up.