Writing a Quadratic Function in Vertex Form A Nature The picture shows the jump of a dolphin. The vertex of the dolphin’s jump is at the point (3, 7). What quadratic function models the path of the dolphin’s jump? B A parabola passes through the point (˛1, ˛1), opens upward, and has an axis of symmetry at x ˚ ˛3 and vertical stretch ... Section 2.2 Characteristics of Quadratic Functions 59 Graphing Quadratic Functions Using x-Intercepts When the graph of a quadratic function has at least one x-intercept, the function can be REMEMBER written in intercept form, f(x) = a(x − p)(x − q), where a ≠ 0. An x-intercept of a graph is the x-coordinate of a point where the graph
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expressions in equivalent forms. They solve quadratic equations by inspection, by completing the square, by factoring, and by using the Quadratic Formula. Some quadratic equations will have complex solutions. Students also graph quadratic functions and analyze characteristics of those functions, including end behavior.
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For example, f(x) = 2is a constant function and f(x) = 2x+1 is a linear function. f(x) x 1 2 f(x) = 2 f(x) = 2x + 1 It is important to notice that the graphs of constant functions and linear functions are always straight lines. We have already said that a quadratic function is a polynomial of degree 2. Here are some examples of quadratic functions: The graph of a quadratic function is a shape called a parabola. The most basic parabola is obtained from the function. The graph of is shown below. The vertex of the graph of is at (0, 0). If the vertex is at some other point on the graph, then a translation or a transformation of the parabola has occurred.