- WE WANT TO SOLVE THE 
FOLLOWING PROBLEM GRAPHICALLY
USING THE GRAPHING CALCULATOR.
NASA LAUNCHES A ROCKET 
AT T = 0 SECONDS.
IT'S HEIGHT IN METERS 
ABOVE SEA LEVEL
AS A FUNCTION OF TIME
IS H OF T = -4.9T SQUARED 
+ 310T + 332.
WE WANT TO ASSUME THAT 
THE ROCKET WILL SPLASH DOWN
IN THE OCEAN.
WE WANT TO ANSWER 
TWO QUESTIONS.
WHAT TIME WILL THE ROCKET 
SPLASH INTO THE OCEAN
AND HOW HIGH ABOVE SEA LEVEL 
WILL THE ROCKET REACH?
WELL, THERE'S A COUPLE THINGS 
WE SHOULD RECOGNIZE
RIGHT AWAY.
FIRST, WE HAVE 
A QUADRATIC FUNCTION
WHICH FORMS A PARABOLA 
OR A U-SHAPE.
IF THIS LEADING COEFFICIENT 
IS NEGATIVE
THE PARABOLA OPENS DOWN
IT WOULD LOOK 
SOMETHING LIKE THIS.
NEXT, THE FUNCTION VALUE 
WHEN T IS = TO 0
IS GOING TO BE 332.
SO THE ROCKET STARTS 
332 METERS ABOVE SEA LEVEL.
AND THEN WE ASSUME IT'S GOING 
TO UP, REACH A HIGH POINT,
COME BACK DOWN, 
AND SPLASH INTO THE OCEAN.
SO LETS SEE 
IF WE CAN GRAPH THIS FUNCTION
ON THE GRAPHING CALCULATOR
AND THEN ANSWER 
THESE TWO QUESTIONS.
ONE OF THE CHALLENGING PARTS 
ABOUT GRAPHING THIS
ON THE GRAPHING CALCULATOR
IS ADJUSTING THE WINDOW TO GET 
A NICE VIEW OF THE FUNCTION.
SO WE'RE GOING TO PRESS =, 
CLEAR OUT ANY OLD FUNCTIONS,
TYPE IN OUR NEW FUNCTION.
INSTEAD OF T WE'LL USE X.
SO -4.9, X IS THIS KEY HERE,
SQUARED IS THIS KEY HERE 
+ 310X + 332.
NOW, LET'S ADJUST THE WINDOW 
BY PRESSING THE WINDOW KEY.
REMEMBER X REPRESENTS THE TIME
AND Y REPRESENTS 
THE HEIGHT OF THE ROCKET.
SO LETS START THE TIME 
AT LETS SAY, I DON'T KNOW, -10
AND LET'S GO OUT 
TO 60 SECONDS,
WHICH WOULD BE 1 MINUTE.
WE HAVE TO ADJUST THESE AGAIN, 
CHANGE THE X SCALE TO 10,
THAT MEANS THERE WILL BE 
A TIC MARK EVERY 10 MINUTES.
THEN FOR THE Y VALUES, WE KNOW 
THE Y INTERCEPT IS 332
SO WE'RE GOING TO HAVE 
A PRETTY LARGE Y MAXIMUM.
LETS START WITH A Y MINIMUM 
OF LET'S SAY -500
AND THEN WE'LL GO LET'S SAY 
A MAXIMUM OF 6,000.
AGAIN, IF THIS DOESN'T WORK
WE CAN ALWAYS COME BACK 
AND ADJUST IT.
LET'S CHANGE THE Y SCALE TO 
500 AND NOW WE'LL PRESS GRAPH.
AND THIS WINDOW 
LOOKS PRETTY GOOD,
BUT LET'S GO AHEAD AND EXTEND 
THE X MAXIMUM FURTHER
SO WE CAN SEE WHERE THIS 
PARABOLA CROSSES THE X AXIS
FOR A SECOND TIME.
SO WE'LL PRESS WINDOW, LET'S 
GO AHEAD AND THE 60 TO 70
AND PRESS GRAPH.
NOW THAT WE HAVE THE GRAPH
I THINK IT'S GOING TO BE 
FAIRLY STRAIGHT FORWARD
TO INTERPRET THIS.
THE ROCKET STARTS AT A HEIGHT 
HERE AT THE Y INTERCEPT,
WHICH IS 332,
AS TIME PASSES IT REACHES 
A MAXIMUM HEIGHT HERE
AT THE VERTEX OF THE PARABOLA
AND THEN IT STARTS 
TO COME BACK DOWN.
AND THIS X INTERCEPT HERE
REPRESENTS WHEN THE ROCKET 
SPLASHES INTO THE OCEAN
BECAUSE THE HEIGHT WOULD BE 0 
OR 0 METERS ABOVE SEA LEVEL.
SO FOR THIS FIRST QUESTION,
WHAT TIME WILL THE ROCKET 
SPLASH INTO THE OCEAN?
WE ACTUALLY WANT TO FIND 
THE X VALUE OR T VALUE,
WHICH WOULD BE 
THIS INTERCEPT HERE.
SO ON THE CALCULATOR WE'RE 
GOING TO PRESS SECOND TRACE
AND THEN THE X INTERCEPTS 
ARE THE 0'S.
WE'RE GOING TO PRESS NUMBER 2.
NOW -- IS FOR THE 
LEFT-BOUND AND RIGHT-BOUND.
SO WE'RE GOING TO MOVE 
THIS CURSER VERY CLOSE
TO THIS X INTERCEPT,
BUT JUST TO THE LEFT OF IT
WHICH IN THIS CASE 
WOULD BE ABOVE IT.
IT'D BE SOMEWHERE IN HERE, 
PRESS ENTER
AND NOW IT'S GOING TO ASK 
FOR THE RIGHT-BOUND,
WHICH IN THIS CASE IS GOING TO 
BE JUST BELOW THE X INTERCEPT.
SO WE'LL PRESS THE RIGHT ARROW
UNTIL THE CURSER 
IS BELOW THE X INTERCEPT.
IT'S HARD TO TELL, 
BUT THIS IS BELOW.
NOTICE HOW THE Y VALUE 
IS NEGATIVE.
SO WE'VE CROSSED THE X AXIS.
PRESS ENTER 
AND THEN ENTER ONE MORE TIME.
SO NOW WE CAN SEE 
AT THE BOTTOM HERE
THAT THE X INTERCEPT 
IS APPROXIMATELY 64.3,
WHICH MEANS THE ROCKET 
WILL SPLASH INTO THE OCEAN
AFTER APPROXIMATELY 
64.3 SECONDS.
NEXT, WE WANT TO KNOW 
HOW HIGH ABOVE THE SEA LEVEL
WILL THE ROCKET REACH.
LET'S GO BACK TO OUR GRAPH.
REMEMBER THE Y VALUES 
REPRESENT THE HEIGHT
SO THE VERTEX 
OR THIS HIGH POINT HERE
WOULD BE THE HIGHEST POINT 
ABOVE SEA LEVEL
THAT THE ROCKET REACHES.
SO NOW WE'RE GOING TO PRESS 
SECOND TRACE AGAIN
FOR THE CALCULATION MENU.
AND NOW SELECT OPTION 4 
FOR MAXIMUM.
AND NOW TO FIND THAT POINT
WE HAVE TO PLACE THE CURSER 
TO THE LEFT
AND THEN TO THE RIGHT 
OF THE VERTEX.
NOW, WE'LL PRESS 
THE LEFT ARROW
UNTIL WE'RE OVER TO THE LEFT 
OF THE VERTEX,
MAYBE SOMEWHERE IN HERE, 
PRESS ENTER,
MOVE IT BACK TO THE RIGHT SIDE 
OF THE VERTEX,
MAYBE SOMEWHERE IN HERE, 
PRESS ENTER,
AND THEN ENTER ONE MORE TIME.
SO HERE ARE THE COORDINATES 
OF THE VERTEX.
THE QUESTION ONLY ASKED 
FOR THE HEIGHT OF THE ROCKET,
WHICH WOULD BE 
THE Y COORDINATE
OR APPROXIMATELY 5,235.1.
AND THE X VALUE REPRESENTS
HOW LONG IT TAKES 
TO REACH THAT POINT,
WHICH IS APPROXIMATELY 
31.63 SECONDS.
BUT AGAIN OUR QUESTION 
ONLY ASKED FOR THE HEIGHT.
SO HERE IS HOW WE CAN SOLVE 
THIS PROBLEM USING TECHNOLOGY.
THE NEXT VIDEO WE'LL TAKE 
A LOOK AT
HOW WE CAN SOLVE THIS BY HAND
USING WHAT WE KNOW 
ABOUT QUADRATIC FUNCTIONS
AND QUADRATIC EQUATIONS.
