SOLUTION: The parabola y = ax^2 + bx + c is graphed below. Find a \cdot b \cdot c. (The grid lines are one unit apart.) The parabola passes through (-5,-13), (2,7), and (4,-5).

Algebra ->  Functions -> SOLUTION: The parabola y = ax^2 + bx + c is graphed below. Find a \cdot b \cdot c. (The grid lines are one unit apart.) The parabola passes through (-5,-13), (2,7), and (4,-5).      Log On


   

Question 1209281: The parabola y = ax^2 + bx + c is graphed below. Find a \cdot b \cdot c. (The grid lines are one unit apart.)
The parabola passes through (-5,-13), (2,7), and (4,-5).
Found 2 solutions by greenestamps, mccravyedwin:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Solving similar problems like this in which the numbers are "nice" gives good practice in using formal mathematical methods. The numbers in this problem are so ugly that using formal methods to find the answer is a huge waste of time.

Go to wolframalpha.com and in the input box enter "equation of parabola through (-5,-13), (2,7), and (4,-5)". It will give you the answer in about 1 second:

y=%28-62%2F63%29x%5E2%2B%28-2%2F21%29x%2B%28701%2F63%29

Now multiply those three coefficients to find the answer to this absurd problem....

Answer by mccravyedwin(407) About Me  (Show Source):
You can put this solution on YOUR website!
Let's plot the points and sketch a parabola through them:



y+=+ax%5E2+%2B+bx+%2B+c

Substitute each point:



Simplify and put the constants on the right.

system%2825a+-+5b+%2B+c=-13%2C%0D%0A4a+%2B+2b+%2B+c=7%2C%0D%0A16a+%2B+4b+%2B+c=-5%29

Subtract the 2nd and 3rd equation from the first
to eliminate c

system%2821a-7b=-20%2C9a-9b=-8%29

Multiply the 1st by 9 and the 2nd by -7 to eliminate b

system%28189a-63b=-180%2C-63a%2B63b=56%29

Add the equations:

126a=-124

a=-124%2F126

a=-62%2F63

Go back to

system%2821a-7b=-20%2C9a-9b=-8%29

Multiply the 1st by 9 and the 2nd by -21 to eliminate a

system%28189a-63b=-180%2C-189a%2B189b=168%29

Add the equations:

126b=-12

b=%28-12%29%2F126

b=-2%2F21

Go back to the easiest one of the original
equations:

4a+%2B+2b+%2B+c=7

4%28-62%2F63%29+%2B+2%28-2%2F21%29+%2B+c=7

-248%2F63-4%2F21%2Bc=7

Multiply through by 63:

-248-12%2B63c=441

-260%2B63c=441

63c=701

c=701%2F63

So abc%22%22=%22%22%28-62%2F63%29%28-2%2F21%29%28701%2F63%29%22%22=%22%2286924%2F83349

Yes, your teacher should be fired, for they do not know how to teach
mathematics.  No competent teacher would assign such a problem as this!

Edwin