Evaluate the function?

Question

Find f(a + 3) when f(x) = x square - 4

Answer 1

Cary, three things you need to know backwards-and-forwards:
a) how to evaluate functions for specific input
b) how to multiply two polynomials
c) two ways to solve quadratic equations

Multiplying (a+3) by (a+3) is similar to multiplying two 2-digit numbers.

  (a + 3)
∙ (a + 3)
  -------
   a² + 3a
           3a + 3²
  -------------------
   a² + 6a + 9


Now you can plug that into f(x) = x² - 4:
f(a+3) = (a+3)² - 4
         =  a² + 6a + 9 - 4
         =  a² + 6a + 5

There are two ways to solve this:
Method 1: Use the Quadratic formula to solve AX²+BX+C=0

X= [-B ± √(B²-4BC)]/(2A)
In this case, A=1, B=6, C=5, so
          a = [-(6) ± √(6² - 4∙1∙5)]/2∙(1)

This gives you two solutions:
          a₊ = -1
          a₋ = -5


The other way to solve this is to set a² + 6a + 5 to 0 and factor it into two polynomials:
          a² + 6a + 5 = (a+1)(a+5)

(a+1)(a+5) = 0 when
          (a+1) = 0 ⇒ a = -1
or
          (a+5) = 0 ⇒ a = -5


If you still don't understand how to approach these types of problems, ask one of your parents to E-mail me and I'll try to explain it better.

Answer 2

f(x)= x square - 4
or f(x) = x^2 - 4
hence f(a+3) =( a+3) ^2 - 4
= a^2+ 9+6*a - 4
= a^2 + 6*a + 5

Answer 3

f(a+3) = (a+3)^2+4 = a^2 + 6a +13

Answer 4

f(x)=x^2 -4
f(x)=(x-2)(x+2)

To evaluate f(a+3) just plug in 'a+3'
f(a+3)=(a+3-2)(a+3+2)=(a+1)(a+5)