Anatomy of a Quadratic Function

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

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

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

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

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

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

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

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

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

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

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

The axis of symmetry passes through the vertex of the parabola

Domain and Range Domain of a parabola is all real numbers

Range of a parabola Depends on where the parabola sits…

Solving Quadratic Functions

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

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

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

4x 2 +13=253

5x 2 -19=231

9(x-2) 2 =121

4(x+2) 2 =49

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

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

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

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

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