Find the standard representation of the following function
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Find the standard representation of the following function
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: Expand the product using the FOIL method:
First terms:
Outer terms:
Inner terms:
Last terms:
This gives us the expression:
Step 2: Combine like terms:
Combine and to get .
Thus, the expression simplifies to:
Therefore, the standard form of the function is .
Create an algebraic expression based on the following parameters:
\( a=3,b=0,c=-3 \)
Sign errors are super common! Remember that (-x) × (x) = -x², not +x². Write out each multiplication step clearly and track negative signs through the entire process.
FOIL is just a memory tool for the distributive property with binomials! It helps you remember to multiply every term in the first binomial by every term in the second.
Look for like terms - terms with the same variable and exponent. In this problem, -3x and +2x are like terms because they both have x¹.
Yes! You could distribute (-x+2) to each term in (x+3), or vice versa. The final answer will be the same as long as you don't miss any terms.
Standard form for quadratic functions is ax² + bx + c. Always arrange your final answer with the highest degree term first: x² term, then x term, then constant.
Pick a simple value like x = 1 and substitute into both the original and expanded forms. If f(1) gives the same result in both forms, your expansion is correct!
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