Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -7x^2 + 9x + 9.

Question

• {-0.78, 1.00}
• {-7,9}
• {-1.29,-1.29}
• {-0.66,1.95}                                                                                                                                                                                                                                                                                                                                                                                                                                                             I think my answer is A. {-0.78, 1.00}.

Answer 1

-7x² + 9x + 9 = 0 has solutions (from the quadratic formula) x = [-9 ± √(81 - 4(-7)(9))]/-14 = -9/(-14) ± √(333)/(-14)
(approximately)= 9/14 ± 1.3034491 = .6428571 ± 1.3034491

.64 + 1.30 = 1.94 and .64 - 1.30 = -.66

So the answer is (-0.66, 1.95)

 

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You can also use an excel spreadsheet to verify

 

 

Answer 2

 - 7 X^2  + 9X + 9 =0

 

   Using Quadratic formula:

 

      -9    ± √(81- 4 ( -7 * 9 )

     -14            - 14

 

       9   ±√(333)

      14       14

 

 

    (- 0.66, 1. 95)

 

    The correct answer is D.

 

 

     

Answer 3

YOU ARE GIVEN THE FUNCTION   f(x) = -7x^2 + 9x + 9  AND 4 (X,Y) PAIRS.  FOR EACH PAIR, SUBSTITUTE THE X INTO F(X) AND CALCULATE TO SEE IF THE RESULT EQUALS THE Y (OR F(X) ) VALUE FOR THE PAIR.  A MATCHING ANSWER INDICATES THAT PAIR IS A VALID SOLUTION.

 

THIS IS A STRAIGHT FORWARD SUBSTITUE AND CALCULATE EXERCISE.  NOTE THAT IT DOES NOT ASK FOR A SOLUTION FOR F(X) = 0.  THAT REQUIRES USE OF THE QUADRATIC EQUATION.

 

GOOD LUCK,  B

 

PS IF YOU THINK {-0.78, 1.00} IS AN ANSWER, SUBSTITUE X=-0.78 INTO -7x^2 + 9x + 9 AND SEE IF THE RESULTING F(X) IS 1.00.  

Answer 4

You use the quadratic formula [-b+sqrt(b^2-4ac)]/2a

-7x^2+9x+9=0

7x^2-9x-9=0

 

[9+sqrt(81-4*7*(-9))]/14

[9+sqrt(81+252)]/14

[9+sqrt(333)]/14    (you can simplify sqrt(333) to 3sqrt(37) but it is not necessary)

(9+18.24828)/14

(9+18.24828)/14=27.24828/14=1.9463

(9-18.24828)/14=-9.24828/14=-0.66059

The last pair is the solution.