Question

Rewrite the function f(x)=3(x+1)^2-2 in the form f(x)=ax^2+bx+c

Answer 1

Step-by-step explanation:

f(x)=3(x+1)^2-2

= 3 [x^2 + 2x + 1 ] -2

=3x^2 + 6x +3-2

=3x^2 + 6x + 1

f(x)=ax^2+bx+c

ax^2+bx+c = 3x^2 + 6x + 1

a = 3

b = 6

c = 1

Answer 2

Answer:

f(x) = 3x² + 6x + 1

General Formulas and Concepts:

• Order of Operations: BPEMDAS
• Expand by FOIL (First Outside Inside Last)
• Standard Form: f(x) = ax² + bx + c
• Vertex Form: f(x) = a(bx + c)² + d

Step-by-step explanation:

Step 1: Define function

f(x) = 3(x + 1)² - 2

Step 2: Find Standard Form

1. Expand by FOILing:                        f(x) = 3(x² + 2x + 1) - 2
2. Distribute 3:                                     f(x) = 3x² + 6x + 3 - 2
3. Combine like terms (constants):    f(x) = 3x² + 6x + 1