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In fact, a quadratic equation is composed as follows:
y = ax²-bx-c
That is,
a is the coefficient of x², in this case 2.
b is the coefficient of x, in this case 5.
And c is the number without a variable at the end, in this case 6.
What is the value of the coefficient \( b \) in the equation below?
\( 3x^2+8x-5 \)
In , the coefficient of x includes its sign. Since we have -5x, the coefficient b = -5. The negative sign is part of the coefficient, not separate!
Always rearrange first! Move all terms to one side so you have or . Then identify your coefficients.
Yes! b and c can be zero, but a cannot be zero in a quadratic function. If a = 0, it becomes a linear function instead.
Use the pattern: a goes with x², b goes with x¹, c goes with x⁰ (the constant). They're in alphabetical order matching decreasing powers!
If a term is missing, its coefficient is zero. For example, means a = 3, b = 0, c = 7 because there's no x term.
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