9.1 quadratic functions

9.1 Quadratic Functions

Algebra 17.0, 21.0

Main Idea & Vocab• This chapter is all about quadratics!• We begin our parabola journey with the basics in this lesson.

• Quadratic equation: written in the form y=ax2 + bx + c.

• Parabola: the curve created when you graph a quadratic equation.

• Vertex: the center point which is the highest or lowest point of a parabola.

Vocabulary

• DomainDomain: the set of all x values of a function.

• RangeRange: the set of all y values of a function.

• FunctionFunction: A relation where every domain value is paired with exactly one range value. One to one!

Quadratics

Ex 1 – Points On the GraphEx. 1: Points on Graph1)Substitute2)Solve3)Yes or No?

Practice 1

Ex 2 –Graphing Quadratics

• Ex. 2 Graphing1)Make a table of at

least 5 points

2) Plug in each xx to find each yy

3) Plot each point and connect with a curve

Practice

Ex 3- Identifying the Direction of a Parabola

• When a quadratic is written in the form y=y=aaxx22 + + bbx + x + cc, the value of a determines the direction the parabola opens!

Practice 3

Ex 4- Minimum & Maximum

Ex 4- Minimum & Maximum

Practice 4

Example 5

• Step 1: Identify the maximum• Step 2: Find the domain and range.

Review

• What is the standard form of a quadratic equation?

• How do you know if a point is on the curve?

• How do you graph a quadratic equation?• How do you identify the direction of a

quadratic equation?• How do you find the minimum and

maximum value of a quadratic?