f(x) = x² + 10x + 29
y = x² + 10x + 29
y - 29 = x² + 10x
y - 29 + 25 = x² + 10x + 25
y - 4 = x² + 5x + 5x + 25
y - 4 = x(x) + x(5) + 5(x) + 5(5)
y - 4 = x(x + 5) + 5(x + 5)
y - 4 = (x + 5)(x + 5)
y - 4 = (x + 5)²
y = (x + 5)² + 4
f(x) = (x + 5)² + 4
Minimum: [tex]x = \frac{-b}{2a} = \frac{-10}{2(1)} = \frac{-10}{2} = -5[/tex]
Maximum: [tex]x = \frac{b}{-2a} = \frac{10}{-2(1)} = \frac{10}{-2} = -5[/tex]
f(x) = (x + 5)² + 4
y = (-5 + 5)² + 4
y = (0)² + 4
y = 0 + 4
y = 4
The local maximum value of the function is located at x = -5.
