posted by on .

1. Explain in detail how to determine the value of the independent variable in a quadratic relation if the value of the dependent variable is known.

You would substitute the value for the dependent variable, then you would solve for the independent variable.
(is it right?)

2. What is the greatest number of solutions a quandratic equation can have? Explain, with an example, why all of the solutions to the equations may not be reasonable answers to the original problem.

A quandratic equations can have either no solution, one solution or two solutions.

Thanks!

1. The independent variable is the "x" in the quadratic equation ax^2 + bx + c = y (the dependent variable)
If you know y, then solve
ax^2 + bx + (c-y) = 0
c-y is a new constant, c'
The equation can be solved by completing the square or using the equation

x = [-b +/- sqrt(b^2-4ac')]/2a

2. You are right; the greatest number of solutions is two. There can be one solution in some cases. It is possible that all solutions contain imaginary numbers (the square root of a negative number), in which case there are no REAL solutions.

It is possible that only one of the two solutions is a reasonable solution to the problem. For example, if you throw a ball and ask when it hits the ground,
y = at - bt^2,
there will be two solutions; one will be the time t=0 when you threw it.