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1310-Notes-Sec-35

# 1310-Notes-Sec-35 - Math 1310 Section 3.5 Maximum and...

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Math 1310 Class Notes – Section 3.5, Page 1 of 6 Math 1310 Section 3.5 Maximum and Minimum Values Next, we’ll look at a specific type of function, the quadratic function . A quadratic function is a function of the form , ) ( 2 c bx ax x f + + = where a, b and c are real numbers and 0 a . We can write a quadratic function in the form k h x a x f + - = 2 ) ( ) ( . This is called the standard or vertex form of the quadratic equation. The graph of a quadratic function is a parabola with vertex ) , ( k h . It will open either upward or downward. If it opens upward, it has a minimum value k . If it opens downward, it has a maximum value k . We can use the graph of the quadratic function to help us find the maximum or minimum value of the function. Our first task will be to change a given quadratic function from the form c bx ax x f + + = 2 ) ( to standard form. We’ll complete the square to do this. Once the function is in standard form, we can sketch a graph using transformations and then read off the maximum or minimum value.

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