Since “ a” is positive (2), this means that the graph opens up and has a minimum at the vertex. *put the equations in descending order (largest exponent first) The general form for a quadratic function is y = ax 2 + bx + c.ĭefining Quadratic Equations: Standard Form with Real Numbers (02:50)īy examining “ a” in f ( x) = ax 2 + bx + c, it can be determined whether the function has a maximum value (opens up) or a minimum value (opens down).Įxample #2: Determine if vertex of the quadratic function is a minimum or a maximum point in its parabola and if the parabola opens upward or downward.Ī.) f ( x) = –5 x + 2 x 2 + 2 b.) g ( x) = 7 – 6 x – 2 x 2 Therefore, the quadratic form is y = 4 x 2–21 x – 18. Multiply the First terms, the Outer terms, the Inner terms, and the Last terms and add them. If given a function, such as f ( x) = (4 x + 3)( x – 6), and asked to express it into quadratic form, use FOIL (First Outer Inner Last) multiplication to write it in the formĮxample #1: Express f ( x) = (4 x + 3)( x – 6) in quadratic form using the FOIL method. Range: all real numbers ≥ the minimum value of the function (when opening up) or all real numbers ≤ the maximum value of the function (when opening down). Vertex: either the lowest point on the graph or the highest point on the graph.ĭomain of any quadratic function: the set of all real numbers. Parabola: the graph of a quadratic functionĪxis of symmetry: a line that divides the parabola into two parts that are mirror images of each other. Introduction to Quadratic Functions Quadratic functions have the form f ( x) = ax 2 + bx + c where the highest exponent is 2.Īre the following functions, quadratic functions? Lastly, you will explore many real-world applications of the quadratic functions and their parabolas. In addition, you will solve quadratic equations using factoring and the Zero Product Property. This unit will introduce you to quadratic functions. For example, fireworks, when fired, follow a parabolic path and many explode when the vertex is reached. Quadratic functions have important applications in science, engineering, and entertainment.
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