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What is a quadratic equation in standard form?
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A quadratic equation in standard form is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
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What is the quadratic formula used for?
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The quadratic formula is used to find the solutions (roots) of a quadratic equation.
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State the quadratic formula.
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The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).
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What does the discriminant in a quadratic equation tell us?
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The discriminant (b² - 4ac) determines the nature of the roots of the quadratic equation.
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What are the possible outcomes for the roots based on the discriminant?
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If b² - 4ac > 0, there are two real and distinct roots; if b² - 4ac = 0, there is one real root (repeating); if b² - 4ac < 0, there are no real roots, only complex roots.
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How many solutions does a quadratic equation have?
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A quadratic equation can have two, one, or no real solutions.
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What is factoring and how is it related to quadratic equations?
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Factoring is a method used to solve quadratic equations by expressing the equation as a product of linear factors.
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Give an example of a simple quadratic equation.
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An example of a simple quadratic equation is x² - 5x + 6 = 0.
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What do we need to do if a quadratic equation cannot be factored easily?
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If a quadratic equation cannot be factored easily, we can use the quadratic formula or complete the square method to solve it.
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Explain completing the square method for solving a quadratic equation.
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Completing the square involves transforming the quadratic equation into a perfect square trinomial, making it easier to solve by taking square roots.
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What does 'quadratic' mean?
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The term 'quadratic' comes from 'quad', meaning square, because the variable is squared (x²).
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Why must 'a' not be zero in a quadratic equation?
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If 'a' were zero, the equation would no longer be quadratic; it would become linear.
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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 graph shape does a quadratic equation form?
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The graph of a quadratic equation forms a parabola.
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What determines the direction of a parabola (upward or downward) in a quadratic graph?
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The sign of 'a' determines the direction: if 'a' is positive, the parabola opens upwards; if negative, it opens downwards.
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