Y
Finish the steps below to write a quadratic function for
the parabola shown.
8
6
1. Use the vertex form, f(x) = a(x - 1)2 + k, and
substitute in the values for h and k.
f(x) = a(x - 5)2 +3
2. Use another point and substitute in values
for x and f(x). Solve for a.
5 = a(6-5)2 + 3
(6 5
4
2
Vertex:
(5, 3)
3. Write the function, using the values for h, k, and a.
х
The function is f(x)
(x
32+
2
4
6
8

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24