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Unformatted text preview: Math 1330 Section 2.1 3 Quadratic Functions A quadratic function is a function which can be written in the form gGÂ¡Â¢ = Â£Â¡ Â¤ + Â¥Â¡ + Â¦ , where a , b , and c are real numbers and a is not equal to zero. The Standard Form of a Quadratic Function Every quadratic function also known as a parabola is written as gGÂ¡Â¢ = Â£Â¡ Â¤ + Â¥Â¡ + Â¦ or can be written in standard form : gGÂ¡Â¢ = Â£GÂ¡ âˆ’ â„ŽÂ¢ + Â§ . The vertex is the point Gâ„Ž,Â§Â¢ . The axis of symmetry is the equation x = h . For a quadratic function, gGÂ¡Â¢ = Â£Â¡ Â¤ + Â¥Â¡ + Â¦ or gGÂ¡Â¢ = Â£GÂ¡ âˆ’ â„ŽÂ¢ Â¤ + Â§ â€¢ The graph opens up if a > 0. â€¢ If Â£ > 1 , is the parabola is narrower; if Â£ < 1 the parabola is wider. The vertex is the turning point of the parabola. If the parabola opens upward the function has a minimum value ( yvalue) . If the parabola opens downward the function has a maximum value ( yvalue) . The axis of symmetry is a line through the vertex that divides the graph in half. The vertex of a parabola whose equation is gGÂ¡Â¢ = Â£Â¡ Â¤ + Â¥Â¡ + Â¦ is Â¨âˆ’ Â¥ 2Â£ ,g Â©âˆ’ Â¥ 2Â£ ÂªÂ« And the axis of symmetry is Â¡ = âˆ’ Â¬ Â¤Â Math 1330 Section 2.1 4 You should be able to identify the following: â€¢ Direction the graphs opens(upwards or downwards) â€¢ Whether the function has a maximum or a minimum â€¢ yintercept â€¢ coordinates of the vertex â€¢ equations of the axis of symmetry â€¢ maximum or minimum Example 5:...
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 Spring '10
 N/A
 Quadratic equation

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