Answer:
f(x) = 4x² + 48x + 149
Step-by-step explanation:
f(x) = 4(x + 6)² + 5
The above expression can be written as: f(x) = ax² + bx + c, by doing the following:
1. Expand (x + 6)²
(x + 6)² = (x + 6)(x + 6)
(x + 6)(x + 6)
x(x + 6) + 6(x +6)
x² + 6x + 6x + 36
x² + 12x + 36
(x + 6)² = x² + 12x + 36
2. Substitute x² + 12x + 36 for (x + 6)² in
f(x) = 4(x + 6)² + 5
This is illustrated below:
f(x) = 4(x + 6)² + 5
(x + 6)² = x² + 12x + 36
f(x) = 4(x² + 12x + 36) + 5
Clear bracket
f(x) = 4x² + 48x + 144 + 5
f(x) = 4x² + 48x + 149
Therefore, the standard of the function:
f(x) = 4(x + 6)² + 5
is
f(x) = 4x² + 48x + 149
