find the minimum and maximum values

Question

Graph the quadratic function. First find your minimum or maximum value, and then create a chart to find your coordinate points.
f(x) = -x2 – 2x + 1

Answer 1

First, determine whether this parabola opens upward, and has a minimum, or opens downward, and has a maximum. Since the first term is negative, this opens downward, so you're finding a maximum.

 

Next, figure out where the vertex is. The axis of symmetry is -b/2a, when you consider the quadratic as f(X) = aX^2+bX+c

 

-b/2a = -(-2)/2(-1) = 2/-2 = -1. So the axis of symmetry is at X=-1. Plug that into your equation to get the y value for the vertex. That will be f(-1) = -(-1^2) - 2(-1) + 1 = -1+2+1 = 2. So the vertex is at (-1,2)

 

Now make a T-chart, with the following X values. Start with the vertex, x=-1. Then put in a couple values for x on either side of the vertex, so you can plot the function. I'd use at least -3, -2, -1, 0, 1 for your input column in your T-chart.

 

--Louise K.