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Chapter 11

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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

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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

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Examples:

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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)

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

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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

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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!!!!

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

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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

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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

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

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GROWTH Compound interest DECAY radioactive

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Quadratic Functions Solving by Graphing Quadratic Function Standard Form: f(x) = ax 2 + bx + c.

Quadratic Functions Solving by Graphing Quadratic Function Standard Form: f(x) = ax 2 + bx + c.

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