Select the function that represents a parabola with vertex at (2,-1) and a point (5,8) on its curve

a.) f(x)=2(x+2)^2-1

b.) f(x)=(x+2)^2-1

c.) f(x)=(x-2)^2-1

d.) f(x)=2(x-2)^2-1

Correct answer is c.)

Step-by-step explanation:

The vertex form of a parabola can be written as following:

is the co-ordinate of vertex.

is a constant whose positive or negative value decides where the parabola opens (up or down).

are the points on parabola.

and are interchangeable terms. We can use any of them.

For convenience with the co-ordinates in plane, is used here.

We are given that vertex is at (2,-1) and there is a point (5,8) on the curve.

i.e. h = 2 and k = -1,

x = 5 and y = 8

Putting the four values in equation (1):

Putting values of and in equation (1) to find the equation of parabola:

As told earlier as well, and are interchangeable terms.

So, correct equation of parabola is option C)

a

step-by-step explanation: