# Chapter 11.  f(x) = ax ² + bx + c, where a ≠ 0 ( why a ≠ 0 ?)  A symmetric function that reaches either a maximum or minimum value as x increases 

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Chapter 11

 f(x) = ax ² + bx + c, where a ≠ 0 ( why a ≠ 0 ?)  A symmetric function that reaches either a maximum or minimum value as x increases  The graph is a parabola  A function in which its solutions can sometimes be found with factoring, can be approximated by graphing, and can always be found using the quadratic formula

 The trajectory of a baseball thrown into the air, a flare shot from a gun, or a diver jumping off of a cliff  The relationship between the length and width of a rectangle while keeping a constant area  Any symmetric relation that decreases to reach a minimum point and then increases

 Examples:

 Symmetric  Line of symmetry  For every y = ax² + bx + c, where a ≠ 0, x = -b / 2a  Vertex  Maximum (sad)  Minimum (happy)  Roots  X-intercept(s)

 Integral roots (integers)  Estimated roots  One distinct root  No real roots (no x-intercept)

 Set the quadratic function equal to zero  Factor if possible  Find the axis of symmetry  Find the coordinates of the vertex  If not factorable, find more points on the graph using a function table. Estimate the roots if applicable

 The solutions of a quadratic equation in the form of ax ² + bx + c = 0, where a ≠ 0 are given by the formula x = -b + √ b² - 4ac 2a For ANY Quadratic Function!!!!

 √b² - 4ac is positive number  2 roots  √b² - 4ac is 0  1 root  √b² - 4ac is negative number  no solution

 An Exponential Function is a function that can be described by an equation in the form of y = a, where a > 0 and a ≠ 1

 The change starts out gradual and then becomes much more significant  The graph is a curve  The exponent is the independent variable which varies while the base stays constant  The base describes the growth or decay of the pattern

 Suppose a is a positive number other than 1.  Then a¹ = a ² if and only if x₁ = x₂

GROWTH  Compound interest DECAY  radioactive

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