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What is the standard form of the function [tex]\( f \)[/tex]?

Given: [tex]\( f(x) = 4(x + 6)^2 + 5 \)[/tex]

Express [tex]\( f(x) \)[/tex] in the form [tex]\( f(x) = ax^2 + bx + c \)[/tex].

Sagot :

GinnyAnswer
To convert the function [tex]\( f(x) = 4(x + 6)^2 + 5 \)[/tex] into its standard form [tex]\( f(x) = ax^2 + bx + c \)[/tex], let's follow the steps of expanding and simplifying the given expression.

1. Expand the binomial:
[tex]\[ (x + 6)^2 = x^2 + 12x + 36 \][/tex]

2. Multiply the binomial term by 4:
[tex]\[ 4(x^2 + 12x + 36) = 4x^2 + 48x + 144 \][/tex]

3. Add the constant 5:
[tex]\[ 4x^2 + 48x + 144 + 5 = 4x^2 + 48x + 149 \][/tex]

The standard form of the function is:
[tex]\[ f(x) = 4x^2 + 48x + 149 \][/tex]

Thus, the coefficients are:
[tex]\[ a = 4, \quad b = 48, \quad c = 149 \][/tex]
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