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

Answer:

Correct answer is c.) \(f(x)=(x-2)^2-1\)

Step-by-step explanation:

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

\(y = a(x-h)^2 + k ....... (1)\)

\((h,k)\) is the co-ordinate of vertex.

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

\((x,y)\) are the points on parabola.

\(y\) and \(f(x)\) are interchangeable terms. We can use any of them.

For convenience with the co-ordinates in \(xy-\)plane, \(y\) 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):

\(8 = a(5-2)^2 + (-1)\\\Rightarrow 8 = a(9) -1\\\Rightarrow 9 = 9a \\\Rightarrow a = 1\)

Putting values of \(a\) and \((h,k)\) in equation (1) to find the equation of parabola:

\(y=(x-2)^2-1\)

As told earlier as well, \(y\) and \(f(x)\) are interchangeable terms.

So, correct equation of parabola is option C) \(f(x)=(x-2)^2-1\)

The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.


Mountain View School Seaside School
0 5, 8
9, 8, 2, 0 1 0, 1, 2, 5, 6, 8
8, 7, 6, 5, 5, 4, 4, 3, 1, 0 2 5, 5, 7, 7, 8
0 3 0, 6
Key: 2 | 1 | 0 means 12 for Mountain View and 10 for Seaside


Part A: Calculate the measures of center. Show all work. (2 points)

Part B: Calculate the measures of variability. Show all work. (1 point)

Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (1 point)

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