Solving Quadratics - All Methods

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What is a quadratic equation?

Back

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 is the quadratic formula?

Back

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

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What does the discriminant tell us about a quadratic equation?

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The discriminant (D = b² - 4ac) indicates the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

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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 are the zeros of a quadratic function?

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The zeros of a quadratic function are the values of x that make the function equal to zero, also known as the roots of the equation.

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How can you solve a quadratic equation by completing the square?

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To solve by completing the square, rearrange the equation to isolate the constant, then add (b/2)² to both sides, and solve for x.

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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 is the axis of symmetry in a quadratic function?

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The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

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How do you find the vertex of a quadratic function?

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The vertex can be found using the formula (h, k) where h = -b/(2a) and k is the value of the function at x = h.

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What is the standard form of a quadratic equation?

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The standard form of a quadratic equation is written as y = ax² + bx + c.