Question 1. Go to random.org. This website is a random numbergenerator. Use it to generate three numbers a, b, c between -10 and10. Now let your a, b and c be the coefficients of the quadraticfunction

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 wouldbef(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 itis 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 findthem.

   Otherwise, explain how you know that it has no realsolutions.

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

   find the complex solutions.

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

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