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Published byLeon Goodman Modified over 5 years ago

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Anatomy of a Quadratic Function

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Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already been looking at quadratics Anything with an x 2 term in the equation

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Creating a quadratic Done by foiling Example (3x+2)(2x-4)

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To be a quadratic… Must have an x 2 term Must have a constant number not equal to zero. Proper form: Ax 2 + Bx +C Practice identifying

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Create the quadratic… Foil to get the quadratic, and label a, b, and c (2x-1)(3x+5)

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Foil to get the quadratic, and label a, b, and c (2x-5)(x-2)

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Quadratic Function How do I know it’s a function?

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The parabola Graph of a quadratic function is a parabola It’s the “U” shape Upward opening parabola- the coefficient with the x 2 term is positive

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Downward opening parabola- The coefficient with the x 2 term is negative

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Axis of Symmetry Each parabola has an axis of symmetry Axis of symmetry- line that divides a parabola into two parts that are mirror images of one another DO IT

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The parabola Vertex- lowest point or highest point on a graph

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Max and Min Values If the parabola opens up, the min value is at the vertex If the parabola opens down, the max value is at the vertex

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The axis of symmetry passes through the vertex of the parabola

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Domain and Range Domain of a parabola is all real numbers

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Range of a parabola Depends on where the parabola sits…

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Solving Quadratic Functions

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Square Roots x 2 =a where a is any number greater than or equal to 0 x is called the square root of a The solution, x has two values

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Properties of Square Roots Positive square root is called the principal root Properties of square roots

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Solve Solve just like a regular equation Follow order of operations, but leave square root till the end Simplify all other ways first

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4x 2 +13=253

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5x 2 -19=231

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9(x-2) 2 =121

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4(x+2) 2 =49

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Warm Up! Complete this problem at the bottom of your sheet Solve 4x 2 +5=20

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Solving using the Calculator Quadratic formulas can have more than one solution Because a square root of a number can give a positive and negative number They can also have no solutions, or just one

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So how do I know if I am right? Use your calculator Solve so the entire equation is set equal to 0 Go to y= on your calculator Plug the equation into y1 Look for the x intercepts of the graph Use the Solve key to find values

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Pythagorean Theorem a 2 + b 2 =c 2 Works only for right triangles What is a right triangle?

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Homework: page286 #15, 18, 21, 24, 27, 30

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