SOLUTION: 1) Explain how you might go about constructing a quadratic equation whose solutions are -5 and 7. 2) The connection between the graph and the equation is an important and he

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: 1) Explain how you might go about constructing a quadratic equation whose solutions are -5 and 7. 2) The connection between the graph and the equation is an important and he      Log On


   

Question 413114: 1) Explain how you might go about constructing a quadratic equation whose solutions are -5 and 7.
2) The connection between the graph and the equation is an important and helpful one! Briefly discuss the effect of the sign of the coefficient a on the graph of y = ax2 + bx + c. Please include two examples of graphs to support your thoughts, one where a < 0 and one where a > 0. (It is encouraged but not required to include the graphs of your examples in your post. If you do not include the actual graphs, please describe your examples in detail with words.)
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

1) Explain how you might go about constructing a quadratic equation whose solutions are -5 and 7.

  The factor theorem states that a polynomial f(x) has a factor (x − k) if and only if f(k) = 0. 

 f(x) = (x+5)(x-7) = 0

 f(x) = x^2 -2x -35



2) Effects of coeficient a on graph of y = a^2 + bx + c

  a > 0  Parabola opens upward (blue)

For example: x^2 + 2x + 1

   a < 0  Parabola opens downward (green)

For example: - x^2 + 2x + 1