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.

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) (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 or

or Start with the given solutions

or Get every term to the left side

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)

FOIL

Combine like terms.

So the equation becomes

Plug in and

Multiply and simplify. Notice how everything cancels out but the "0.67"

Multiply and simplify. Notice how everything cancels out but the "0.67"

Divide both sides by -0.67 to isolate "a"

So the constant is

Plug in into the equation

Distribute

Multiply

So the equation that goes through the three points is

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