SOLUTION: The sign of the discriminant D is positive as the parabola opens upward. We observe the x intercepts to be –1, and 0.67 So the function is written as y = a(x – (-1)) (x – 0.67) w

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The sign of the discriminant D is positive as the parabola opens upward. We observe the x intercepts to be –1, and 0.67 So the function is written as y = a(x – (-1)) (x – 0.67) w      Log On


   

Question 106110: The sign of the discriminant D is positive as the parabola opens upward.
We observe the x intercepts to be –1, and 0.67
So the function is written as y = a(x – (-1)) (x – 0.67) where ‘a’ is a constant.
y = a (x + 1) (x – 0.67)
The lowest point of the parabola is the vertex.
Now the parabola passes through (- 0.16, -2)
-2 = a( - 0.16 + 1) ( - 0.16 – 0.67)
-2 = a(0.84) (- 0.83)
a = -2/ (0.84)(- 0.83)
a = 2.87
Thus the quadratic equation is y = 2.87 ( x + 1) (x – 0.67)
Or y = 2.87 (x2 + 0.33x – 0.67)
The quadratic equation is 2.87 ( x2 + 0.33x – 0.67 ) = y
To solve for x, we equate y to 0.
x2 + 0.33x – 0.67 = 0
x2 + 0.33x – 0.67 = 0
x2 + x – 0.67 x – 0.67 = 0
x (x + 1) – 0.67 ( x + 1) = 0
(x + 1) (x – 0.67) = 0
X + 1 = 0 or x – 0.67 = 0
X = -1 or x = 0.67
The solution is x = -1 or x = 0.67
This is a discussion group question. One of the girls on my team came up with this but I can't figure out where she got the 0.33x. I thought I was getting it but now I am confused. Can you explain this? Please, Please!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Look at this part of the discussion when you multiplied the factors together.
y=2.87%28x%2B1%29%28x-0.67%29
Use the FOIL method (First Outer Inner Last)
%28x%2B1%29%28x-0.67%29=x%2Ax%2Bx%2A%28-0.67%29%2B%281%29x%2B%281%29%28-0.67%29
%28x%2B1%29%28x-0.67%29=x%5E2%2Bx%2Ahighlight%28%281-0.67%29%29-0.67
%28x%2B1%29%28x-0.67%29=x%5E2%2Bhighlight%280.33%29x-0.67
I hope this answers your question.