Find the roots of the following quadratic functions. (a) f(x) = 3x^2 - x - 10 (b) g(x) = 8x^2 - 22x - 21 Complete the square to find the minimum or maximum value of the following quadratic functions. (a) f(x) = x^2 + 4x + 1 (b) y = x^2 - 8x + 21 (c) y = 3x^2 + 12x + 16 (d) g(x) = - 2x^2 + 16x - 33 (e) h(x) = 9x^2 - 12x + 6 (f) y = 25x^2 + 10x + 4 For what value(s) of c does the function f(x) = x^2 + cx - 9 have a double root? No real roots? Suppose f(x) is any quadratic function and let c be an arbitrary constant. Are the following statements true or false? Explain your answer using graphs. (a) There is a unique value of c such that the function y = f(x) + c has a double root? (b) There is a unique value of c such that the function y = f(x) + c has 2 distinct real roots? (c) There is a unique value of c such that the function y = f(x + c) has a double root? (d) There is a unique value of e such that the function y = f(x + c) has 2 distinct real roots?
