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What is a quadratic function?
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A quadratic function is a type of polynomial function with the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.
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What is the graph of a quadratic function called?
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The graph of a quadratic function is called a parabola.
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What shape does the parabola take if a > 0?
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If a > 0, the parabola opens upwards and looks like a 'U' shape.
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What happens to the parabola if a < 0?
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If a < 0, the parabola opens downwards and looks like an upside-down 'U' shape.
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What is the vertex of a parabola?
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The vertex is the highest or lowest point on the parabola, depending on whether it opens upwards or downwards.
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How do you find the vertex of a quadratic function in standard form?
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For the equation y = ax² + bx + c, the vertex can be found using the formula (-b/2a, f(-b/2a)).
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What is the axis of symmetry in a parabola?
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The axis of symmetry is a vertical line that passes through the vertex of the parabola, given by the equation x = -b/2a.
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What are the roots of a quadratic equation?
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The roots are the values of x that make the quadratic equation equal to zero, also known as the solutions or x-intercepts.
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How can you find the roots of a quadratic function?
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Roots can be found using the quadratic formula, factoring, or by completing the square.
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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 roots of ax² + bx + c = 0.
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What does the discriminant tell us about the roots of a quadratic function?
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The discriminant (b² - 4ac) indicates the nature of the roots: two real and distinct if positive, one real and repeated if zero, and two complex if negative.
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How does changing the value of 'b' affect the parabola?
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Changing 'b' affects the position of the vertex and the axis of symmetry but does not affect the direction the parabola opens.
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What role does 'c' play in the quadratic equation y = ax² + bx + c?
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The 'c' value represents the y-intercept of the parabola.
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How can you express a quadratic function in vertex form?
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A quadratic function in vertex form is expressed as y = a(x-h)² + k, where (h, k) is the vertex.
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How do you convert a quadratic equation to vertex form?
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To convert to vertex form, you complete the square to rewrite y = ax² + bx + c as y = a(x-h)² + k.
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