quadratic functions and equations ch. 4.1 quadratic functions and transformations eq: how can i...

EQ: HOW CAN I GRAPH A QUADRATIC FUNCTION? I WILL ACCURATELY GRAPH A QUADRATIC FUNCTION.

QUADRATIC FUNCTIONS AND

EQUATIONS

Ch. 4.1Quadratic Functions and Transformations

BELL WORK

EQ: HOW CAN I GRAPH A QUADRATIC FUNCTION? I WILL ACCURATELY GRAPH A QUADRATIC FUNCTION.

FYI- Current

Q1 grades

are posted in the back.

QUADRATIC FUNCTIONS AND TRANSFORMATIONS

READ

When considering transformations, we may wonder whether they can transform the graph of a quadratic function so that the parabola opens leftward or rightward. The graph can be transformed this way, for example, by a reflection in y=x.

Understand that the graph of any quadratic function is a transformation of the graph of the parent function, x=x^2. The axis of symmetry is a line that divides the parabola in to two mirror images.

Special note- Do not confuse the absolute value graph with a parabola.

EQ: HOW CAN I GRAPH A QUADRATIC FUNCTION? I WILL ACCURATELY GRAPH A QUADRATIC FUNCTION.

THE PARENT QUADRATIC FUNCTION

EQ: HOW CAN I GRAPH A QUADRATIC FUNCTION? I WILL ACCURATELY GRAPH A QUADRATIC FUNCTION.

CONCEPT SUMMARY

EQ: HOW CAN I GRAPH A QUADRATIC FUNCTION? I WILL ACCURATELY GRAPH A QUADRATIC FUNCTION.

GRAPHING A FUNCTION OF THE FORM F(X) = AX2

EQ: HOW CAN I GRAPH A QUADRATIC FUNCTION? I WILL ACCURATELY GRAPH A QUADRATIC FUNCTION.

EQ: HOW CAN I GRAPH A QUADRATIC FUNCTION? I WILL ACCURATELY GRAPH A QUADRATIC FUNCTION.

GRAPHING A FUNCTION FOR THE FORM F(X) = AX2

Now you try…

KEY CONCEPT

EQ: HOW CAN I GRAPH A QUADRATIC FUNCTION? I WILL ACCURATELY GRAPH A QUADRATIC FUNCTION.

EQ: HOW CAN I GRAPH A QUADRATIC FUNCTION? I WILL ACCURATELY GRAPH A QUADRATIC FUNCTION.

STOP AND TALK

What can you say about the graph of a quadratic function if a is negative?

Describe what a vertex is, and how to find it.

Describe what an axis of symmetry is, how does knowing this help you graph a quadratic?

EQ: HOW CAN I GRAPH A QUADRATIC FUNCTION? I WILL ACCURATELY GRAPH A QUADRATIC FUNCTION.

GRAPHING THE TRANSLATION OF F(X) = X2

EQ: HOW CAN I GRAPH A QUADRATIC FUNCTION? I WILL ACCURATELY GRAPH A QUADRATIC FUNCTION.

GRAPHING THE TRANSLATION OF F(X) = X2

Now you try…

EQ: HOW CAN I GRAPH A QUADRATIC FUNCTION? I WILL ACCURATELY GRAPH A QUADRATIC FUNCTION.

TRANSLATION OF THE PARABOLA

EQ: HOW CAN I GRAPH A QUADRATIC FUNCTION? I WILL ACCURATELY GRAPH A QUADRATIC FUNCTION.

USING VERTEX FORM

EQ: HOW CAN I GRAPH A QUADRATIC FUNCTION? I WILL ACCURATELY GRAPH A QUADRATIC FUNCTION.

USING VERTEX FORM

EQ: HOW CAN I GRAPH A QUADRATIC FUNCTION? I WILL ACCURATELY GRAPH A QUADRATIC FUNCTION.

WRITING A QUADRATIC FUNCTION IN VERTEX FORMIf the parabola of a vertex is at (4, 5) and the parabola is not compressed or stretched vertically, what is the equation of this quadratic function?

EQ: HOW CAN I GRAPH A QUADRATIC FUNCTION? I WILL ACCURATELY GRAPH A QUADRATIC FUNCTION.

CLOSURE

(On your bell sheet)

Compare and Contrast

Describe the difference between the graphs of

y = (x + 6)2 and y = (x – 6)2 + 7