Final answer:
To write the standard form of a quadratic function with an a-value of 2 and a root of 5 + 2i, use the conjugate pair property.
Step-by-step explanation:
To write the standard form of a quadratic function with an a-value of 2 and a root of 5 + 2i, we can use the fact that complex roots come in conjugate pairs. Since 5 + 2i is a root, its conjugate, 5 - 2i, is also a root. Therefore, the quadratic function can be written as:
f(x) = a(x - (5 + 2i))(x - (5 - 2i))
Substituting the value of a = 2, we get:
f(x) = 2(x - (5 + 2i))(x - (5 - 2i))