Five Question Mixed Review 1. What is this function: y= 3x-2 2. What is the y-intercept of the above equation? 3.Solve for x: 16 = 5x What is the slope of this equation: y= ½ x Write this equation in function notation: y = 6p - 7

Five Question Mixed Review--Key 1.Linear = 5x = 5x 3 = x or x = 3 15 = 5x 4.½ 5.f(p) = 6p - 7

Parabolas: Nature or by Design Ideas?

Can you find the parabolic shapes?

Standard and Essential Questions MM1A1b: Graph the basic functions f(x) = x n Essential Question: Can you identify a quadratic function by its components?

Could you predict what it will look like with just 2 points? Is the slope constant? If not, what is it? Does it point up or down? What shape? How is it different from a linear graph?

What is a parabola? KEY NOTE CARD: A parabola is the U-shaped graph. It can be pointing up (positive slope) or pointing down (negative slope).

A quick look at an equation The most basic quadratic formula is y = x 2 it is called a parent graph. This means that the U shape (a parabola) is turned up and the vertex is at (0,0).

This is a quadratic parent graph. Notice where the vertex is located (0,0) The equation for this graph Is y = x 2 Remember: A vertex is where the quadratic graph turns and shifts direction. It is also called a critical point.

What does an input/output chart look like for this parent graph? xy Ponderables What do you notice? Do x values repeat? Do y values repeat? What do you call an image like this? Can you see the vertex? What do you notice about the slope?

What Changed? The vertex moved! It moved up by one unit! When a number is changed here, it shows how the graph moves up and down.

This quadratic graph moved DOWN one unit. New vertex: (0, -1)

Name that shift!

Name this shift!

Shifting up and down along the y-axis is called vertical shift. BUT you can also shift left and right along the x-axis? What is it called?

This is called a horizontal (left/right) shift. The parent graph shifted to the left 1 unit. The new equation would look like this: y = (x+1) 2 Horizontal movement is always inside the parentheses with the x. These equations have a trick though— you move in the opposite direction! New vertex: (-1,0)

Name that shift! What kind is it? What is the new vertex?

Name this shift! What kind is it? What is the new vertex?

This graph shifts both ways! What is the vertical shift? What is the horizontal shift? What is the vertex?

How about this one? What is the vertical shift? What is the horizontal shift? What is the vertex? Notice how the equation matches the vertex except for the opposite sign inside the parentheses?

Identifying the Slope IT’S A FACT: In a parent graph the vertex is at (0,0) and the slope of the FIRST reflective points are 1. The rest of the slope is VARIABLE or CHANGING Slope = 1 Slope = 3 Slope = 5 Slope = rise/run =

What happens if the slope is more than 1? Slope = 4 How does it compare to the parent graph?

Slope = -4 What happened?

Slope = ½ How does this compare to the parent graph?

Slope = -½ How does this compare to the last graph?

Parts of a Quadratic Equation y- intercept vertical shift = _2__ Slope = __2_ Horizontal shift = _2__ (Opposite of x vertex value) Vertex can be found at (2, 2) When the slope is larger than 1 then the graph becomes…

Graphic Organizer: Parts of a Quadratic Equation _________ _______shift _______ shift (Opposite of__ vertex value) Vertex can be found at (__, __) ______

Parts of a Quadratic Equation y- intercept vertical shift= ___ Slope = ___ Horizontal shift=___ (Opposite of x vertex value) Vertex can be found at (__, __)

Parts of a Quadratic Equation y- intercept vertical shift= ___ Slope = ___ Horizontal shift=___ (Opposite of x vertex value) Vertex can be found at (__, __) When the slope is smaller than 1 then the graph becomes…

Parts of a Quadratic Equation y- intercept vertical shift= ___ Slope = ___ Horizontal shift=___ (Opposite of x vertex value) Vertex can be found at (__, __) Does it matter how large the numbers are?

Get with a partner to do these! Directions: Identify the a)Slope b)y-intercept c)Vertex AND Graph 1 of these!

Partner task--Key Directions: Identify the a)Slope b)y-intercept c)Vertex AND Graph 1 of these! Ex. y=x 2 -2

Quiz Graphing Quadratic Functions 1-8. Choose the function rule that matches the graph. Put the letter in the blank. 9)Which of the graphs above is the parent graph for quadratic functions? #______ 10)How many graphs have a negative slope?____

Quiz Graphing Quadratic Functions--Key 1-8. Choose the function rule that matches the graph. Put the letter in the blank. 9)Which of the graphs above is the parent graph for quadratic functions? #___4___ 10)How many graphs have a negative slope?__2__

Extending/Refining

Go back to photographs Identify all of the parabolas you see and state whether they have a positive slope or a negative slope!