Ex: Quadratic Function Application – Blood Pressure


– 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.  

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