- HEALTHY AVERAGE SYSTOLIC BLOOD 
PRESSURE IS ESTIMATED
BY P = 0.01A 
SQUARED = 0.05A + 107
WHERE "A" IS THE AGE IN YEARS
AND P IS THE PRESSURE 
IN MILLILITERS OF MERCURY.
NUMBER 1, WHAT IS THE HEALTHY 
AVERAGE SYSTOLIC BLOOD PRESSURE
OF A 34-YEAR-OLD 
TO THE NEAREST 10th?
SO TO DETERMINE THE PRESSURE,
WE'LL SUBSTITUTE 34 FOR "A" 
INTO OUR EQUATION.
SO P OF 34 IS GOING TO BE EQUAL
TO 0.01 x 34 SQUARED 
+ 0.05 x 34 + 107.
AND WE'LL GO AHEAD 
AND USE THE CALCULATOR
TO DETERMINE THIS VALUE.
SO 0.01 x 34 SQUARED 
+ 0.05 x 34 + 107.
NOW, THEY WANT US TO ROUND 
TO THE NEAREST 10th,
SO THIS WILL BE APPROXIMATELY 
120.3 MILLILITERS OF MERCURY.
NUMBER 2 IS GOING TO BE A LITTLE 
BIT MORE INVOLVED.
IF A HEALTHY PERSON 
HAS A SYSTOLIC BLOOD PRESSURE
OF 132.4 MILLILITERS OF MERCURY,
WHAT IS THEIR AGE 
TO THE NEAREST YEAR?
SO WE'RE GOING TO NEED SOME MORE 
ROOM FOR THIS.
LET'S GO AHEAD 
AND GO TO THE NEXT SLIDE.
FOR THIS PROBLEM, THEY'RE GIVING 
US THE PRESSURE, P,
AND WE NEED TO SOLVE FOR "A."
SO WE NEED TO SOLVE 
THE EQUATION
132.4 = 0.01A SQUARED 
+ 0.05A + 107,
SO WE HAVE QUADRATIC EQUATION.
SO WHAT WE'RE GOING TO DO HERE 
IS SET IT EQUAL TO 0
AND USE THE QUADRATIC FORMULA.
SO WE'LL START 
BY SUBTRACTING 132.4
ON BOTH SIDES OF THE EQUATION,
SO WE'LL HAVE 0 = 0.01A 
SQUARED + 0.05A, 107 - 132.4
IS GOING TO BE 
NEGATIVE OR MINUS 25.4.
AND NOW TO APPLY THE QUADRATIC 
FORMULA,
"A" IS THE COEFFICIENT 
OF THE DEGREE 2 TERM,
SO WE'LL HAVE = 0.01,
B IS THE COEFFICIENT 
OF THE DEGREE 1 TERM, 0.05,
AND C IS EQUAL TO THE CONSTANT 
TERM OF -25.4.
NOW USING THE QUADRATIC FORMULA 
GIVEN HERE BELOW,
WE WILL HAVE X = -B OR -0.05
PLUS OR MINUS THE SQUARE ROOT OF 
B SQUARED - 4 x "A" x C
ALL OVER 2 x "A" 
WHICH WOULD BE 2 x 0.01.
NOW ONE THING TO BE AWARE OF 
HERE, HERE WE'RE SAYING X EQUALS
BUT WE SHOULD RECOGNIZE THAT OUR 
EQUATION IS IN TERMS OF "A",
SO THIS IS REALLY "A" EQUALS,
NOT TO BE CONFUSED 
FOR THIS "A" HERE
THAT WOULD BE THE COEFFICIENT 
OF THE DEGREE 2 TERM.
SO JUST TO AVOID CONFUSION,
WE'LL GO AHEAD 
AND CONTINUE WITH X.
WE'LL HAVE X = -0.05
PLUS OR MINUS 
THE SQUARE ROOT OF.
NOW, WE'LL DETERMINE 
THE DISCRIMINANT HERE
AND THIS WOULD BE DIVIDED 
BY 2 x 0.01 OR 0.02,
SO OUR DISCRIMINANT 
WILL BE 0.05 SQUARED - 4 x "A"
WHICH IS 0.01 x C 
WHICH IS - 25.4,
SO WE HAVE 1.0185.
NOW REMEMBER, WE ARE GOING
TO HAVE 2 SOLUTIONS HERE.
BUT SINCE THIS X VALUE OR "A" 
VALUE REPRESENTS THE AGE,
WE KNOW THE AGE 
CAN'T BE NEGATIVE,
SO THE ONLY POSSIBLE SOLUTION 
WOULD BE
X = -0.05 + THE SQUARE ROOT OF 
1.0185 DIVIDED BY 0.02.
AND THEY WANT THIS 
TO THE NEAREST YEAR,
SO NOW WE'LL GO BACK 
TO THE CALCULATOR
TO DETERMINE 
THIS APPROXIMATE VALUE.
SO TO DO THIS, 
WE'LL HAVE A SET OF PARENTHESES
FOR THE NUMERATOR.
WE'LL HAVE AN OPEN PARENTHESIS
-0.05 + THE SQUARE ROOT 
OF 1.0185.
NOTICE WE HAVE ONE CLOSED 
PARENTHESIS FOR THE SQUARE ROOT
AND THE SECOND ONE 
FOR NUMERATOR,
AND I'M GOING TO DIVIDE THIS 
BY 0.02.
SO WE HAVE APPROXIMATELY 
47.96 YEARS
WHICH WOULD ROUND 
TO 48 YEARS OF AGE.
OKAY I HOPE 
YOU FOUND THIS HELPFUL.
