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.

1 is c

2 is a

3 is a

step-by-step explanation: