Question

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

Answer 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) $f(x)=(x-2)^2-1$