Determine the equation of the parabola graphed below.

Vertex Form: f(x) = (x - 4)² + 1

Standard Form: f(x) = x² - 8x + 17

Step-by-step explanation:

Standard Form: ax² + bx + c = 0

Transformations Graph: f(x) = a(bx - c)ⁿ + d

a = vertical shrink/stretch

b = horizontal shrink/stretch

c = horizontal movement left/right

d = vertical movement up/down

(c, d) is vertex

Step 1: Define variables

Vertex (4, 1)

c = 4

d = 1

(Since we are dealing with a quadratic) n = 2

Step 2: Set up equation

f(x) = a(x - 4)² + 1

Step 3: Find a (vertical shrink/stretch)

Order of Operations: BPEMDAS

Point (3, 2) on given graph

Plug in the point to find a.

Step 4: Write Vertex Form

f(x) = 1(x - 4)² + 1

f(x) = (x - 4)² + 1

Step 5: Convert to Standard Form

Step 5: Check

Graph the newly founded equation.

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.