Chapter 5: Exercises with Solutions

Chapter 5Quadratic FunctionsLastly, to find the y-intercept, set x = 0 in the equation and solve for y:f(x) = x 2 + 6x − 3f(0) = 0 2 + 6(0) − 3f(0) = −3So the y-intercept is (0, −3). Finally, put this all together to make the graph.20yf(x)=(x+3) 2 −12x=−3((−6− √ 48)/2,0) ((−6+ √ 48)/2,0)(−6,−3)(0,−3)x10(−3,−12)To find the domain of f, mentally project every point of the graph onto the x-axis, asshown on the left below. This covers the entire x-axis, so the domain= (−∞, ∞). Tofind the range, mentally project every point of the graph onto the y-axis, as shown onthe right below. The shaded interval on the y-axis is range= [−12, ∞).y20 f(x)=(x+3) 2 −12y20 f(x)=(x+3) 2 −12x10x10(−3,−12)21. First, complete the square:Version: Fall 2007