Problem 1. Write the following functions in the form f(x) = a(x±h)2±k by completing the square. Describe how x2 is shifted to obtain f(x). Graph f(x), label the vertex, label all axis intersections. An example of what I expect is given below.
(a) f(x) = −2x2+8x+10
(b) f(x) = 3x2−12x+2 (c) f(x) = −2x2+3x+2
Example.
Then is the function x2 shifted left units, stretched vertically by a factor of 2, reflected about the x-axis, and shifted up units. To find x-intercepts, we set f(x) = 0 and solve for x:
Note that is positive and is negative. To find the y-intercept, we set x = 0 and find f(0) = −2(0)2 −5(0)+1 = 1. Thus our y-intercept is at y = 1. Noting that our vertex is above the x-axis, on the left of the y-axis, and that the parabola is flipped so that it opens down, it makes sense that one of our x-intercepts is positive and the other is negate. Be sure that all intercepts are labeled and that the vertex is indicated as in the graph below.
