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Quadratic Equation and Graphs
Quadratic Functions and Their Graphs A quadratic function is a polynomial function of degree 2, typically written in the form: $$f(x) = ax^2 + bx + c$$ where a, b, and c are constants and a ≠ 0. Important Properties of Quadratic Function Graphs Y-Intercept: The point where the parabola crosses the y-axis (0, c) X-Intercepts: Also known as zeros, roots, or solutions - points where the parabola crosses the x-axis Vertex: The highest or lowest point of the parabola Axis of Symmetry: A vertical line that passes through the vertex, dividing the parabola into two symmetrical halves Forms of Quadratic Functions 1. Standard Form $$f(x) = ax^2 + bx + c$$ To find the axis of symmetry: $$x = -\frac{b}{2a}$$ 2. Vertex Form $$f(x) = a(x - h)^2 + k$$ Where (h, k) is the vertex of the parabola Characteristics of Parabolas If a > 0, the parabola opens upward (U-shaped) If a The larger the absolute value of a, the narrower the parabola...
