Understanding Quadratic Equations

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What is a quadratic equation?
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A quadratic equation is a second-degree polynomial equation that can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants.
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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 ax^2 + bx + c = 0.
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What does the 'a' variable in a quadratic equation affect?
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The 'a' variable affects the direction and width of the parabola; if 'a' is positive, the parabola opens upward, and if negative, it opens downward.
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What is the quadratic formula?
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The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), used to find the roots of a quadratic equation.
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What does the term 'roots of the equation' mean?
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The roots of the equation are the solutions or values of x that satisfy the quadratic equation.
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How can you determine the number of roots a quadratic equation has?
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By calculating the discriminant (b^2 - 4ac); if it's positive, there are two roots, if zero, one root, and if negative, no real roots.
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What is the discriminant in a quadratic equation?
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The discriminant is the part of the quadratic formula under the square root: b^2 - 4ac. It indicates the nature of the roots.
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What is factoring in relation to quadratic equations?
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Factoring is a method to simplify a quadratic equation by expressing it as a product of its linear factors.
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What are 'perfect square trinomials' in quadratic equations?
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Perfect square trinomials are quadratic equations that can be factored into a binomial squared. They take the form (ax + b)^2.
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What is completing the square?
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Completing the square is a method to solve quadratic equations by converting them into a perfect square trinomial.
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How do you recognize a quadratic equation by its graph?
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A quadratic equation graph is a parabola, a U-shaped curve that can open up or down depending on the coefficient of x^2.
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What is the vertex of a parabola?
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The vertex is the highest or lowest point of the parabola, depending on its orientation, and can be found at (-b/(2a), f(-b/(2a))).
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How do you solve a quadratic equation by graphing?
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Solve by graphing the equation and locating the x-values (roots) where the parabola intersects the x-axis.
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What is the axis of symmetry in a quadratic equation?
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The axis of symmetry is a vertical line that divides the parabola into two mirror images, given by x = -b/(2a).
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What are real and complex roots in quadratic equations?
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Real roots have non-imaginary values and appear on the x-axis; complex roots involve imaginary numbers when the discriminant is negative.
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