Create an algebraic expression based on the following parameters:
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Create an algebraic expression based on the following parameters:
To formulate the quadratic expression using the given parameters, we follow these steps:
Here’s how we perform each step:
Step 1: We start with the formula: .
Step 2: Substitute the given values: .
Step 3: This simplifies to since adding zero does not change the expression.
Thus, the algebraic expression representing the quadratic function with the given parameters is .
What is the value of the coefficient \( b \) in the equation below?
\( 3x^2+8x-5 \)
The standard form gives us a systematic way to write any quadratic expression. The coefficients a, b, and c tell us about the shape, direction, and position of the parabola when graphed.
When c = 0, the constant term disappears from the expression. This means the parabola passes through the origin (0,0) when graphed, since there's no vertical shift.
The standard order is highest degree first: x² terms, then x terms, then constants. So is preferred over .
Double-check each coefficient: a=-1 goes with x², b=2 goes with x, c=0 is the constant. Then verify: .
That's a common error! Remember that a = -1, so the x² term must be negative. Always pay extra attention to negative coefficients when substituting.
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