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what is general equations of quadratic?
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what is general equations of quadratic?
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The general equation of a quadratic function is typically expressed as:
\[ ax^2 + bx + c = 0 \]
Here:
- \(x\) is the variable.
- \(a\), \(b\), and \(c\) are constants where \(a\) is not equal to zero. They determine the shape, direction, and position of the parabola.
The solutions to this quadratic equation can be found using the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
The term inside the square root, \(b^2 - 4ac\), is called the discriminant. The discriminant determines the nature of the solutions:
- If \(b^2 - 4ac > 0\), there are two distinct real solutions.
- If \(b^2 - 4ac = 0\), there is one real solution (a repeated root).
- If \(b^2 - 4ac < 0\), there are two complex conjugate solutions.
This quadratic equation represents a parabola when graphed, and its solutions (roots) are the x-coordinates where the parabola intersects the x-axis.
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