Find the standard representation of the following function
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Find the standard representation of the following function
To convert the function to its standard form, follow these steps:
Step 1: Expand the binomial .
This simplifies to:
Combining these terms gives:
Step 2: Add the constant term to the expanded form:
Step 3: Simplify the expression:
Thus, the standard representation of the function is .
Create an algebraic expression based on the following parameters:
\( a=2,b=2,c=2 \)
When you square a negative, it becomes positive! (-x)² = (-x) × (-x) = x². Think of it like (-3)² = (-3) × (-3) = 9, not -9.
Use FOIL or remember: First² + 2(First)(Last) + Last². For (-x + 1)²: First = -x, Last = 1, so (-x)² + 2(-x)(1) + 1² = x² - 2x + 1.
Vertex form shows the vertex clearly: f(x) = a(x - h)² + k. Standard form is expanded: f(x) = ax² + bx + c. Both represent the same function!
Absolutely! Try x = 1: Original gives (-1 + 1)² + 3 = 0 + 3 = 3. Standard form gives 1² - 2(1) + 4 = 1 - 2 + 4 = 3. They match!
Write out each step carefully! For (-x + 1)², list: (-x)² = x², 2(-x)(1) = -2x, 1² = 1. Then combine: x² - 2x + 1.
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