SOLUTION: Create the quadratic equation in the form ax squared + bx + c using the point (-1,7) as one point and the point (10,-8) as the vertex. enter a,b,c values as common fractions in r

Algebra ->  Rational-functions -> SOLUTION: Create the quadratic equation in the form ax squared + bx + c using the point (-1,7) as one point and the point (10,-8) as the vertex. enter a,b,c values as common fractions in r      Log On


   

Question 37236: Create the quadratic equation in the form ax squared + bx + c using the point
(-1,7) as one point and the point (10,-8) as the vertex. enter a,b,c values as common fractions in reduced form.

i have several problems just like this to answer. i need to know how to come up with the equation. please help. cheryl mitchell clm031303@yahoo.com
Found 2 solutions by AnlytcPhil, stanbon:
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
Create the quadratic equation in the form 
y = ax² + bx + c using the point (-1,7) as one
point and the point (10,-8) as the vertex. 
Enter a,b,c values as common fractions in 
reduced form. 

We start out with the standard form:

y = a(x - h)² + k where the vertex is 
(h, k) = (10, -8).  Substituting:

y = a(x - 10)² - 8

Now this must go through the point (-1, 7), 
so substitute -1 for x and 7 for y, and 
solve for a:

           7 = a(-1 - 10)² - 8

           7 = a(-11)² - 8

           7 = a(121) - 8

           15 = 121a

       15/121 = a

Now y = a(x - 10)² - 8 becomes

    y = 15/121(x - 10)² - 8

Clear of fractions temporarily by multiplying 
both sides by 121:

   121y = 15(x - 10)² - 968

   121y = 15(x² - 20x + 100) - 968

   121y = 15x² - 300x + 1500 - 968

   121y = 15x² - 300x + 532

Divide through by 121

      y = (15/121)x² - (300/121)x + 532/121

a = 15/121, b = -300/121, c = 532/121

Edwin
AnlytcPhil@aol.com

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Create the quadratic equation in the form ax squared + bx + c using the point
(-1,7) as one point and the point (10,-8) as the vertex. enter a,b,c values as common fractions in reduced form.
Because the vertex is (10,-8),
-b/2a=10
Then b=-20a
Rewrite the equation as follows:
y=ax^2-20ax+c
Using the point (-1,7) you get:
7=a+20a+c
Using the point (10,-8) you get:
-8=100a-200a+c
Rewriting both of these you get two equations in a and c, as follows:
7=21a+c
-8=-100+c
Subtracting the 1st from the 2nd you get:
15=121a or a=15/121
Substituting that back you can solve for c which is c=532/121
Substituting back into y=ax^2-20ax+c you get the equation you want:
y=(15/121)x^2-(300/121)x+(532/121)
Cheers,
Stan H.