Problem 1. Write the following polynomials in the form a(x±h)2±k using the method we covered in class (by completing the square). Show all your work. (The ± just means that the signs don’t have to be a certain way, just do whatever’s natural.)
(a) x2+2x+3
(b) 2x2−4x+1
(c) 2x2+3x−2
(d) −3x2+2x+1
(g) 5x2+7x−2
(h) −5x2−3x+7
(k) ax2+bx+c
Problem 2. Check your answers from Problem 1 by converting them back into the form ax2±bx±c.
Problem 3. Show that both and solve the equation ax2+bx+c = 0 by separately plugging each in for x. It may (or may not) be easier to write these as and
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