Question

Question 1. Go to random.org. This website is a random number generator. Use it to generate three numbers a, b, c between -10 and 10. Now let your a, b and c be the coefficients of the quadratic function

f(x)=ax2 +bx+c.

(For example, if the numbers you generated happened to be a = 2,b = 12, c = −1, your function for the rest of the question would bef(x) = 2x2 +12x−1.)

1. (a) Put f(x) into “standard” or “vertex” formf(x)=a(x−h)2 +k.

2. (b) Identify the location of the vertex and determine whether it is a local minimum or local maximum.

3. (c) From the “standard form” determine whether the equationf(x) = 0

   has any real solutions. If it has real solutions then find them.

   Otherwise, explain how you know that it has no real solutions.

4. (d) Use the quadratic formula to confirm what you found in (c). If the equation has no real solutions then use the quadratic formula to

   find the complex solutions.

Question 2. By changing one of your coefficients a, b, c in Question 1, create a quadratic that has a different number of real roots. That is, if your function had no real roots then your goal is to change it to one which does have real roots. If your function did have real roots then your goal is to build one which has no real roots. Once you have created a quadratic function which is what you are looking for (either

with or without real roots), repeat Question 1 using it.

Answer 1