Given the function, f(x) = x^2 + 6x + 3, do the following. a) Does the graph of the parabola open up or down ? b) Find the vertex. Write as an ordered pair. c) Find the y-intercept. Write as an ordered pair. d) Find the x-intercepts (if any). Write as (an) ordered pair(s). e) Identify the axis of symmetry. Write as an equation. f) Sate the domain and range of the function.

## Answer

Answer:

F(x) = x^2 + 6x + 3 (a) we can write f(x) = 1 x^2 + 6x + 3 implies a = 1, b = 6, c = 3 Here the leading coefficient a = 1 greaterthan o since a greaterthan 1 therefore parabola opens up. (b) For vertex we find x = -b/2a implies x = -6/2 (1) = -3 plugging x = -3 in f(x) = x^2 + 6x + 3 we get f (- 3) = (- 3)^2 + 6 (- 3) + 3 = 9 – 18 + 3 = -6 Hence vertex is given by (- 3, – 6) (c)For y – intercept we plug x = 0 in f(x) implies f(0) = 0^2 + 6(0) + 3 = 3 Hence y – intercept is (0,3) (d)For x – intercept we plug y = 0 and solve for x o = x^2 +