Answer:
D
Step-by-step explanation:
Given a quadratic function in standard form
f(x) = ax² + bx + c ( a ≠ 0 )
• If a > 0 then minimum value
• If a < 0 then minimum value
For
f(x) = x² + 16x + 3
a = 1 > 0 then f(x) has a minimum value
The minimum is the value of the y- coordinate of the vertex.
The x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
Here a = 1 and b = 16 , then
[tex]x_{vertex}[/tex] = - [tex]\frac{16}{2}[/tex] = - 8
To find the y- coordinate of the vertex, substitute x = - 8 into f(x)
f(- 8) = (- 8)² + 16(- 8) + 3 = 64 - 128 + 3 = - 61
Thus the function has a minimum value of - 61 → D