Solving Quadratics- All Methods

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What is a quadratic equation?

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A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

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What are the methods to solve quadratic equations?

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The methods to solve quadratic equations include factoring, completing the square, using the quadratic formula, and the square root method.

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What is the quadratic formula?

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The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation.

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When is the square root method applicable?

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The square root method is applicable when the quadratic equation can be expressed in the form x² = k, where k is a constant.

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How do you factor a quadratic equation?

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To factor a quadratic equation, find two numbers that multiply to ac (the product of a and c) and add to b (the coefficient of x).

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What does completing the square involve?

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Completing the square involves rewriting a quadratic equation in the form (x - p)² = q, making it easier to solve.

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What is the vertex form of a quadratic equation?

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The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

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What are the x-intercepts of a quadratic function?

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The x-intercepts of a quadratic function are the points where the graph intersects the x-axis, corresponding to the solutions of the equation.

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What is the discriminant in a quadratic equation?

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The discriminant is the expression b² - 4ac in the quadratic formula, which determines the nature of the roots.

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What does a positive discriminant indicate?

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A positive discriminant indicates that the quadratic equation has two distinct real roots.