



How does the 'b' term affect the horizontal shift of the parabola from its parent function y = ax²? What is the parent function of a quadratic equation?
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what is the b in a quadratic equation Informational
- How does the sign of 'b/2a' determine the horizontal shift of the vertex?
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- Exponential growth is often approximated by quadratics initially. How does 'b' relate to the initial growth rate? How does the 'b' term appear in the solution of certain second-order linear differential equations with constant coefficients?
- How can a quadratic term with coefficient 'b' capture non-linear relationships in financial markets?
- The roots of a quadratic are related by symmetries. How does 'b' influence these symmetries?
- If a quadratic equation arises from a discrete dynamical system, what does 'b' represent in the update rule?
- In numerical analysis, when fitting a parabola to three data points, how do the 'b' coefficient arise in the system of equations? If you have three points (x1, y1), (x2, y2), (x3, y3) that lie on a parabola y = ax² + bx + c, write down the system of equations to solve for 'a', 'b', and 'c'.
- How does the gradient of a quadratic function relate to 'b'? What is the gradient of f(x) = ax² + bx + c?
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