Quadratic Function

Quadratic Function

by Venus Daydayan

​Recall

​Domain- set of all first elements of the ordered pairs.

​ - known as abscissa (x)

Range - set of all second elements of the ordered pairs.

​ - known as ordinate (y)

​A function is a correspondence between the elements of the domain and the elements of the range such that each element of the domain corresponds to exactly one element in the range.

​x

y

Multiple Choice

Is the image shown at left is a function?

• yes

• no

Multiple Choice

Is the image shown at left is a function?

• yes

• no

Multiple Choice

Is the image shown at left is a function?

• yes

• no

​The bridge resembles a common graph with a smooth U-shape called a parabola.

Please watch in my screen first, do not open the video on your tab to avoid confusion.

​Vertex

• ​the turning point of the graph

• ​an ordered pair with coordinates (h,k) where                        and

• ​called a minimum point if the graphs opens upward or ​maximum point if the graph opens downward.

​minimum point (0,0)

​maximum point (0,0)

​If a > 0, the parabola opens upward = the vertex is the lowest point

​if a <0 the parabola opens downward = the vertex is the highest point

​After this slide, this will lead you to the Geogebra board. Please click the button " open in new tab".

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Multiple Choice

Previously, you click the circle under the $$f\left(x\right)=-4x^2$$  , what is the concavity?

• facing upward

• facing downward

Multiple Choice

What is the vertex of   $$f\left(x\right)=-4x^2$$  ?

• (0, 0)

• none

Multiple Choice

Click the circle of $$g\left(x\right)=4x^{2\ \ }-5$$  , what is the vertex of the function?

• (0, -5)

• (-5,0)

Multiple Choice

What is/are the x-intercept of the function: $$g\left(x\right)=4x^{2\ \ }-5$$  ?

• x = -1 and 1

• x = -1.1 and 1.1

Multiple Choice

What is/are the y-intercept of the function: $$k\left(x\right)=-\frac{1}{2}x^2-4x\ +1$$  ?

• y = 1

• y = -1

Multiple Choice

What is the range of the function:   $$k\left(x\right)=-\frac{1}{2}x^2-4x\ +1$$  ?

• $$x\ \in R$$  

• $$y\ \in R$$  

Multiple Choice

What is the range of the function:   $$k\left(x\right)=-\frac{1}{2}x^2-4x\ +1$$  ?

• $$y=9$$  

• $$y\ge9$$  

• $$y\le9$$  

Multiple Choice

Look at the image at the left, what is the vertex point of the graph? is it minimum or maximum point?

• Maximum point     (5, 0)

• Minimum point

  (0, 5)

• Maximum point

  (0,5)

Multiple Choice

Determine the x-intercept

• (0,2)and (0,0)

• (2, 0 )and (0,0)

• (-2, 0 )and (0,0)

• (0,-2)and (0,0)

Second Day

​Sketch and compare the graphs of

​by using Desmos App

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What is the opening/concavity of the graphs?

​Let's have the waterfalls chat, type your answer in the chatbox. When I say WATERFALLS CHAT GO!, you press enter.

​Graph of...

• ​ is narrower than the graph of g(x) =

• ​ is wider than the graph of of g(x) =

​Sketch and compare the graphs of

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​What have you noticed to the graph?

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