Question

F(x) = x2 + 2x - 2 Show graph

Answer 1

Answer:

Step-by-step explanation:

f(x) = x2 + 2x - 2  should be rewritten using " ^ " to indicate exponentiation:

f(x) = x^2 + 2x - 2.

We find a couple of key points and use the fact that this parabola is symmetric about the line

          -2

x = ----------- = -1.  When x = -1, y = f(-1) = (-1)^2 + 2(-1) - 2, or 1 - 2 -2, or -3.

        2(1)

Thus the vertex is at (-1, -3).  The y-intercept is found by letting x = 0:  y = -2.  The axis of symmetry is x = -1.

Graph x = -1 and then reflect this y-intercept (0, -2) about the line x = -1, obtaining (-2, -2).  If necessary, find 1 or two more points (such as the x-intercepts).

To find the roots (x-intercepts), set f(x) = x^2 + 2x - 2 = 0 and solve for x.

Completing the square, we obtain x^2 + 2x + 1 - 2 = + 1, or (x + 1)^2 = 3.

Taking the square root of both sides yields x + 1 = ±√3.  One of the two roots is x = 1.732 - 1, or 0.732, so one of the two x-intercepts is (0.732, 0).