SOLUTION: Given that a quadratic goes through the points (-1,0), (0.67,0), and (0,-2), find the quadratic that goes through the points and find the solutions.

Algebra ->  Graphs -> SOLUTION: Given that a quadratic goes through the points (-1,0), (0.67,0), and (0,-2), find the quadratic that goes through the points and find the solutions.      Log On


   

Question 155148: Given that a quadratic goes through the points (-1,0), (0.67,0), and (0,-2), find the quadratic that goes through the points and find the solutions.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Since there are two real solutions, this means that the discriminant is greater than zero. Since the x-intercepts are (-1,0) and (0.67,0) this means that the solutions are x=-1 or x=0.67

x=-1 or x=0.67 Start with the given solutions


x%2B1=0 or x-0.67=0 Get every term to the left side


a%28x%2B1%29%28x-0.67%29=0 Use the zero product property to join the two equations. I'm introducing the term "a" to make sure that the quadratic goes through the point (0,-2)


a%28x%5E2-0.67x%2Bx-0.67%29=0 FOIL


a%28x%5E2%2B0.33x-0.67%29=0 Combine like terms.


So the equation becomes y=a%28x%5E2%2B0.33x-0.67%29


-2=a%280%5E2%2B0.33%280%29-0.67%29 Plug in x=0 and y=-2


-2=a%28-0.67%29 Multiply and simplify. Notice how everything cancels out but the "0.67"


-2=a%28-0.67%29 Multiply and simplify. Notice how everything cancels out but the "0.67"


3=a Divide both sides by -0.67 to isolate "a"

So the constant is a=3

y=3%28x%5E2%2B0.33x-0.67%29 Plug in a=3 into the equation


y=3%28x%5E2%29%2B3%280.33x%29-3%280.67%29 Distribute


y=3x%5E2%2Bx-2 Multiply

So the equation that goes through the three points is y=3x%5E2%2Bx-2