xy a.o.s.: vertex: max. or min.? x – intercepts y – intercepts

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SOLVING QUADRATICS BY GRAPHING INVESTIGATION AND WORD PROBLEMS

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Page 1: XY A.O.S.: Vertex: Max. or Min.? X – Intercepts Y – Intercepts

SOLVING QUADRATICS BY GRAPHING

INVESTIGATION AND WORD PROBLEMS

Page 2: XY A.O.S.: Vertex: Max. or Min.? X – Intercepts Y – Intercepts

WARM – UP!!• AS YOU WALK IN, PLEASE PICK UP YOUR CALCULATOR AND

START WORK ON THE WARM- UP!

1. WHAT IS THE SPECIAL NAME FOR A QUADRATIC GRAPH? WHAT SHAPE DOES IT HAVE?

2. GRAPH . FILL IN THE TABLE AND THE IMPORTANT INFORMATION BELOW:

X YA.O.S.:

Vertex:

Max. or Min.?

X – Intercepts

Y – Intercepts

Page 3: XY A.O.S.: Vertex: Max. or Min.? X – Intercepts Y – Intercepts

EXAMPLE 2: GRAPH THE FOLLOWING USING THE PROVIDED TABLES AND FILL IN THE IMPORTANT INFO. F(X)=X2 - 6X+9

Axis of Symmetry:

Vertex:

Max or Min?

x-intercepts:

y-intercept:

X -1 0 1 2 3

Y

Page 4: XY A.O.S.: Vertex: Max. or Min.? X – Intercepts Y – Intercepts

EXAMPLE 3: GRAPH THE FOLLOWING USING THE PROVIDED TABLES AND FILL IN THE IMPORTANT INFO. F(X)=-X2+4X-3

Axis of Symmetry:

Vertex:

Max or Min?

x-intercepts:

y-intercept:

X -1 0 1 2 3

Y

Page 5: XY A.O.S.: Vertex: Max. or Min.? X – Intercepts Y – Intercepts

SOLVING QUADRATICS BY GRAPHING INVESTIGATION

• USE YOUR BOOKLET STARTING ON PAGE 25.

• WORK THROUGH PARTS I TO IV AND THEN WE WILL DISCUSS:

WHAT DO MY FACTORS TELL ME ABOUT MY GRAPH? WHAT DO MY X – INTERCEPTS TELL ME ABOUT MY GRAPH?

WHAT DID YOU NOTICE ABOUT THE FACTORS FROM PART I AND THE X – INTERCEPTS FROM PART III?

Page 6: XY A.O.S.: Vertex: Max. or Min.? X – Intercepts Y – Intercepts

SOLVING QUADRATICS BY GRAPHING INVESTIGATION CONTINUED

• CONTINUE WITH PARTS XI AND XII. FOLLOW THE INSTRUCTIONS IN YOUR BOOKLET FOR THE CALCULATOR KEYSTROKES.

• LET ME KNOW IF YOU HAVE QUESTIONS WITH USING THE CALCULATOR OR GRAPHING!

Page 7: XY A.O.S.: Vertex: Max. or Min.? X – Intercepts Y – Intercepts

QUADRATICS + WORD PROBLEMS….YAY!

Suppose a toy rocket was launched straight up into the air from the ground with an initial velocity of 96 feet per second.

The height of the rocket in feet, h, is related to the time in

seconds, t, after the rocket has been launched. The

approximate height of the rocket can be modeled by the

quadratic equation:

.

y=-16 +961. Fill in the table and graph the equation

Page 8: XY A.O.S.: Vertex: Max. or Min.? X – Intercepts Y – Intercepts

QUADRATICS + WORD PROBLEMS CONTINUEDY=-16 +96

2. How many seconds after the rocket was launched did it reach it maximum point?3. What was the maximum height of the rocket?4. How many seconds after the rocket was launched did it hit the ground?5. How high is the rocket after 2 seconds?6. How many seconds have gone by is the rocket is 128 feet in the air?

Page 9: XY A.O.S.: Vertex: Max. or Min.? X – Intercepts Y – Intercepts

QUADRATICS STATIONS ACTIVITY

•USING YOUR HALF SHEET, GO AROUND TO EACH QUESTION AND SEE IF YOU CAN FIGURE OUT WHAT NEEDS TO BE SOLVED FOR.

• THERE SHOULD BE 10 QUESTIONS AND ANSWERS!

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