SOLUTION: The line of symmetry of the parabola whose equation is y = ax^2 - 4x + 3 is x = -2. What is the value of "a"? it has to be one of the following. -2 -1 -1/2

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The line of symmetry of the parabola whose equation is y = ax^2 - 4x + 3 is x = -2. What is the value of "a"? it has to be one of the following. -2 -1 -1/2      Log On


   

Question 749332: The line of symmetry of the parabola whose equation is y = ax^2 - 4x + 3 is x = -2. What is the value of "a"?
it has to be one of the following.
-2
-1
-1/2
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
? The average of the roots would be -2, also.
Let the roots be the variables, r and s.

r=%284-sqrt%2816-4%2A3%2Aa%29%29%2F%282a%29 and s=%284%2Bsqrt%2816-4%2A3%2Aa%29%29%2F%282a%29
r=%284-sqrt%2816-12a%29%29%2F%282a%29 and s=%284%2Bsqrt%2816-12a%29%29%2F%282a%29
r=%284-sqrt%284%2A4-4%2A3a%29%29%2F%282a%29 and s=%284%2Bsqrt%284%2A4-4%2A3a%29%29%2F%282a%29
r=%284-2%2Asqrt%284-3a%29%29%2F%282a%29 and s=%284%2B2%2Asqrt%284-3a%29%29%2F%282a%29
r=%282-sqrt%284-3a%29%29%2Fa and s=%282%2Bsqrt%284-3a%29%29%2Fa

Knowing what the sum of these roots must be,
-2=%28r%2Bs%29%2F2
-4=r%2Bs
-4=%282-sqrt%284-3a%29%2B2%2Bsqrt%284-3a%29%29%2Fa
-4=%282%2B2%2B0%29%2Fa
-4=4%2Fa
-1=1%2Fa
The Answer-------------highlight%28a=-1%29-----------------