Question

Which graph represents the function f(x)=(x-5)^2+3

Answer 1

Step-by-step explanation:

Please find the attachment.

We have been given a function formula $f(x)=(x-5)^2+3$. We are asked to graph the given function.

We know that standard form of parabola is in format $y=a(x-h)^2+k$, where, (h,k) represents the vertex of parabola.

Upon looking at our given formula, we can see that it represents an upward opening parabola as leading coefficient is positive. The vertex of our given parabola will be at point $(5,3)$.

Upon graphing our given function we will get our required function as shown in the attached image.

Answer 2

Answer:

Parabola

Step-by-step explanation:

We are given that a function

$f(x)=(x-5)^2+3$

The given function is an equation of parabola along y- axis.

General equation of parabola along y- axis  with vertex (h,k) is given by

$(y-k)=(x-h)^2$

$y=(x-h)^2+k$

Compare it with given equation then we get

h=5, k=3

Vertex of given parabola =(5,3)

Substitute x=0 then we get

$f(0)=(0-5)^2+3=28$

y-intercept of parabola is at (0,28).