quadratics scavenger hunts

GRAPHING QUADRATIC FUNCTIONS NAME:______________________________________ PERIOD:__________ Date:______________________

WHAT ARE THE KEY FEATURES OF THE GRAPH AND EQUATION OF QUADRATIC FUNCTIONS?

A function can be represented in the form of is called a standard form of quadratic function.

The terms a, b and c, are constants(coefficients) where a≠0. The greatest exponent of the variable x is 2.

The most basic quadratic function is , which is the parent function.

1) a)Complete the table of values for b) Plot the ordered pairs as points on the The parent function.(You can use graph, and connect the points to sketch your graphing calculator) a curve. (arrowheads at the end)

x f(x)=x2

-3

4-10 01 123

a= b= c=

2) a)Complete the table of values for b) Plot the ordered pairs as points on the The

function graph, and connect the points to (You can use your graphing calculator) sketch a curve. (arrowheads at the end)

x f(x)=-4 16-3-2 0-10 -81234 05


a= b= c=

3) a)Complete the table of values for b) Plot the ordered pairs as points on the

The function graph, and connect the points to (You can use your graphing calculator) sketch a curve.(Arrowheads at the end)

a= b= c=


The function graph, and connect the points to (You can use your graphing calculator) sketch a curve.(Arrowheads at the end)

a= b= c=

x f(x)=-101234

x f(x)=-4-3-2-101


A function can be represented in the form of is called a vertex form of a quadratic function. Where (h,k) is the vertex(turning point) of the graph (Parabola) and a≠0. To convert a quadratic function in vertex form to standard form you multiply out and combine like terms. Hint ( if the sign inside the parenthesis is -, h is positive if the sign inside the parenthesis is positive

5. a)Complete the table of values for b) Plot the ordered pairs as points on the

function graph, and connect the points to (You can use your graphing calculator) sketch a curve.(Arrowheads at the end)

a= h= k=

6. a)Complete the table of values for b) Plot the ordered pairs as points on the


xf(x)=

0123456

xf(x)=

0123456


a= h= k=

7. a)Complete the table of values for b) Plot the ordered pairs as points on the The


a= h= k=



x

f(x)=-6-5-4-3-2-1012


a= h= k=

A function can be represented in the form of is called a factored form of a quadratic function. Where (p,0) and (q,0) are the roots, x-intercepts, zeros, solutions of the graph (Parabola) and a≠0. To change a quadratic function in factored form to standard form you multiply out and combine like terms.



a= p= q=



xf(x)=

-10123

x f(x)=-3-2-10123


a= p= q=

x f(x)=-4-3-2-1012




a= p= q=



a= p= q=

x f(x)=01234

xf(x)=

-5-4-3-2-10123


SCAVENGER HUNT QUADRATICS FUNCTIONS IN STANDARD FORM f(x)= ax2 +bx +c

The shape of a quadratic function is called a PARABOLA. It has many features that are associated with its equation: 1)The vertex of the parabola: The vertex is highest or lowest point (x,y) on the graph , also called the turning point. If the parabola opens Up the vertex is called a Minimum, when the parabola opens down the vertex is a Maximum.For problems 1-4 Identify the VERTEX. (use red colored pencil)

On the graphs find the highest or lowest point, write its coordinate (x,y). Write down if the vertex is a maximum or minimum.

On the table of values, look for the y-coordinate that does not repeat and where other y-coordinates repeat above and below this point. Place a red colored arrow next to the point and write down Vertex next to it.

The vertex can also be found from the equation. The x-coordinate is found by using the

values of a and b from the equation: , then substitute this x into the equation to obtain the y- coordinate.

2) The AXIS OF SYMMETRY: is a vertical line through the vertex, where all the points on the parabola mirror each other from each side. The equation of the line of symmetry is the x-

coordinate of the vertex. For problems 1-4 Identify the Axis of Symmetry (A.O.S). (use blue colored pencil)

On the graph, use a ruler a to draw a dashed vertical line through the vertex, label the line A.O.S, x= # of x-coordinate ( Ex: if vertex is (4,2) The A.O.S, x=4) What do you notice about the points on the graph at the right or left of A.O.S?

________________________________________________________________________ On the table of values, find the vertex and circle the x-coordinate of the vertex, label it

A.O.S. On the equation, find the work you did to find the x-coordinate of the vertex and circle

it, label it A.O.S.3) The x-INTERCEPTS: are the points or point where the parabola crosses the x-axis( where the y-coordinate equals to zero). A parabola can have one, two or no real numbers as x-intercepts. It is important to know that other names for roots are: SOLUTIONS, ROOTS, ZEROS.For problems 1-4 Identify the X-INTERCEPTS. (use green colored pencil)

On the graph, find the points where the parabola touches the x-axis, colored and label them with their (x,yI Coordinates.


On the table of values, find the y-coordinates equal to zero, and circle the x,y coordinates write down zeros next to them.(Hint: Use the table of values in the calculator if necessary)

***On the equation, we will use algebraic methods on our next lessons to find the zeros ,x-intercepts, solutions to the equation. In the meantime, learn how to use the TI-84/CASIO to find the zeros from the graph.

a)Write down the equation on Y1, then press graph . If necessary, adjust the graph using Zoom to see where the graph touches the x-axis

b) Press 2nd - Trace (Calc) - press Option 2 : Zeros

c) Move the spider to left point where the graph touches the x-axis. Left Bound? Move the cursor using where the y-coordinate shown below the screen is positive(Above x-axis) press enter, then move the cursor down using , where the y-coordinate shown below is negative(below the x-axis), press enter . Then move the spider closer to the root and press enter. Write down the (x,0) coordinates shown on the screen.

d) If the graph touches twice the x-axis repeat b) above on the other point. Move the spider to right point where the graph touches the x-axis. Left Bound? Move the cursor using where the y-coordinate shown below the screen is negative(below x-axis) press enter, then move the cursor down using , where the y-coordinate shown below is positive(above the x-axis), press enter . Then move the spider closer to the root and press enter. Write down the (x,0) coordinates shown on the screen.

4) The Y-INTERCEPT: is the point where the parabola crosses the y-axis( where the x-coordinate equals to zero). A parabola has one y-intercepts.

For problems 1-4 Identify the Y-INTERCEPT. (use orange colored pencil)

On the graph, find the point where the parabola touches the y-axis, colored and label them with its (x,y) Coordinates.

On the table of values, find the x-coordinate equal to zero, and circle the x,y coordinates write down y-intercept next to them.(Hint: Use the table of values in the calculator if necessary, then write down the point (0,Y-int)

On the equation, find the C value draw an arrow and label the point(0,C) y-intercept.

Questions to think about?

1) How can you use the equation to know if the graph of the quadratic function opens Up or opens Down? How is the a value related to this?

2) What is the Domain ( X-Values) and the range( Y-Values) of the function?


SCAVENGER HUNT QUADRATICS FUNCTIONS IN VERTEX FORM 1)The vertex of the parabola: The vertex is highest or lowest point (x,y) on the graph , also called the turning point. If the parabola opens Up the vertex is called a Minimum, when the parabola opens down the vertex is a Maximum.For problems 5-8 Identify the VERTEX. (use red colored pencil)

On the graphs use the same procedure as the standard form. On the table of values. use the same procedure as the standard form. The vertex can also be found from the equation. Write down The vertex next to the

equation, which is the point (h,k) . Example

a ) Vertex( 5,-3) b) Vertex(-1,0)2) The AXIS OF SYMMETRY: For problems 5-8

Identify the Axis of Symmetry (A.O.S). (use blue colored pencil)

On the graph. Use the same procedure as the standard form. On the table. Use the same procedure as the standard form. The equation of the axis of symmetry is the x-coordinate of the vertex x=h, Example

a ) Vertex( 5,-3) A.O.S -> X=5

3) The X-INTERCEPTS: SOLUTIONS, ROOTS, ZEROS.

For problems 5-8 Identify the X-INTERCEPTS. (use green colored pencil)

On the graphs use the same procedure as the standard form. On the table of values. use the same procedure as the standard form. To Find the Zeros from the vertex form equation will be explored in our next lessons.

For now practice finding the Zeros using the graphing calculator with the procedure explained in the standard form. Before.

4) The Y-INTERCEPT:


On the graphs use the same procedure as the standard form. On the table of values. use the same procedure as the standard form. On the equation, substitute 0 for x and solve for y then write down (0,___) as y-

intercept. Questions to think about?

a) How can you know from the equation if the parabola opens Up or down?b) What do you notice about the position of a graph that has an equation such as y= (x-3)2 and

y= (x+3)2 . (Hint use your graphing calculator to graph both functions)?c) What do you notice about the position of a graph that has an equation such as y= (x-3)2 +5 and

y= (x-3)2 -5 . (Hint use your graphing calculator to graph both functions)d) What is the Domain ( X-Values) and the range( Y-Values) of the function?


SCAVENGER HUNT QUADRATICS FUNCTIONS IN FACTORED FORM

1)The vertex of the parabola: The vertex is located exactly in the middle of the roots. For problems 9-12 Identify the VERTEX. (use red colored pencil)

On the graphs use the same procedure as the standard form. On the table of values. use the same procedure as the standard form. The vertex in factored form can be found from the equation. For x-coordinate use the

midpoint formula , then substitute the x value in to the equation to the equation to find y.

2) The AXIS OF SYMMETRY: For problems 9-12

Identify the Axis of Symmetry (A.O.S). (use blue colored pencil)

On the graph. Use the same procedure as the standard form. On the table. Use the same procedure as the standard form. The equation of the axis of symmetry is the x-coordinate of the vertex =

3) The X-INTERCEPTS: SOLUTIONS, ROOTS, ZEROS.

For problems 9-12 Identify the X-INTERCEPTS. (use green colored pencil)

On the graphs use the same procedure as the standard form. On the table of values. use the same procedure as the standard form. To Find the Zeros from the vertex form equation will be explored in our next lessons.

For now practice finding the Zeros using the graphing calculator with the procedure explained in the standard form. Before.

4) The Y-INTERCEPT:


On the graphs use the same procedure as the standard form. On the table of values. use the same procedure as the standard form. On the equation, substitute 0 for x and solve for y then write down (0,___) as y-

intercept.

Questions:

a) What is the Domain ( X-Values) and the range( Y-Values) of the function?

You can find the vertex (maximum and minimum), Using the TI-83/84 by first entering the function in y1, press graph, (Zoom to adjust the screen) 2nd #3 minimum (Open Up) or #4 maximum (Open down) . Move the spider to the left (Use <) of the vertex and press enter for left bound. Move the spider to the right side of the vertex (use >)Press enter. Move the spider as close to the vertex and press enter for Guess. Write down the (x,y) shown on the screen


Intervals of Increasing or decreasing, Concave UP/Concave downWriting equation in vertex form from the graph.Recognize quadratic from a table finding the second differences

quadratics scavenger hunts

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