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) 2×2 − 4x + 1 (c) 2×2 + 3x − 2
(d) −3×2 +2x+1 (e) 41×2+x−1
(f) 3×2 − 21 x + 3 (g) 5×2 + 7x − 2 (h) −5×2 −3x+7
(i) 12×2+13x+15
(j) 2×2 − 31 x − 1 (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 −b + b2−4ac and −b − b2−4ac solve the equation ax2 + bx + c = 0 by 2a 2a 2a 2a √
separately plugging each in for x. It may (or may not) be easier to write these as −b+ b2−4ac and √ 2a
−b− b2−4ac. 2a
