Write the standard form of a quadratic function with an a-value of 2 and a root of 5+2i.

AnswerOh god-

Step-by-step explanation:

Step-by-step explanation:

The standard form for a factored quadratic is:

Where a is the leading coefficient and p and q are all roots.

Remember that by the Complex Conjugate Root Theorem, if a+bi is a root, then a-bi must also be a root.

Since 5+2i is a root, then 5-2i is also a root.

Hence, we can substitute this for our p and q.

We will also substitute 2 for a. Therefore:

Distribute:

Distribute further:

Distribute:

Combine like terms:

Cancel possible terms. Remember that i²=-1. Hence:

Simplify:

Distribute. So, our equation is:

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .

∠cbe and ∠deb are same-side interior angles.

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