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

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

In your proposed answer, substituting 1.00, you get -7 + 9 + 9 = 11.  This is not even close to zero, so this answer is obviously not correct.

-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

- 7 X^2  + 9X + 9 =0

-9    ± √(81- 4 ( -7 * 9 )
-14            - 14

9   ±√(333)
14       14

(- 0.66, 1. 95)

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.

Hi Bruce, I did what you said to do, but I am coming up with something different each time. I struggle with this type of Math. Did you come up with one of the answers posted above, or can you show me how you did it? Thanks in advance.
Walter; look at my solution. I used the quadratic formula and came up with 1.9463 which is approx. 1.95
and -0.66059 which is approx. -0.66 which is the last pair in your list of solutions. You don't have to substitute; too easy to make a mistake and too time consuming. Use the quadratic formula and you will get the two solutions right away.
Walter,

You can use an Excel or Numbers spreadsheet to check the answers by substitution.  Just set two cells for x and x2, one for each value of x.   Then four new cells: -7x2 and 9x, two for each value of x.  Then two cells for the value of the function.  Then by substituting the values of x in the two cells for each selection you should be able to see which solution works.
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.