Anatomy of a Quadratic Function Quadratic Form Any
- Slides: 28
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 (3 x+2)(2 x-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 ¢ (2 x-1)(3 x+5) ¢
Foil to get the quadratic, and label a, b, and c ¢ (2 x-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 just like a regular equation ¢ Follow order of operations, but leave square root till the end ¢ Simplify all other ways first ¢
4 x 2 +13=253
5 x 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 4 x 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 y 1 ¢ 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: page 286 ¢ #15, 18, 21, 24, 27, 30
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