Sketch the graph of the quadratic function. (Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.)
f(x) = x^2 + x - 8
Indicate the coordinates of the vertex, the y-intercept, and the x-intercepts (if any). (If an answer does not exist, enter DNE. If there are multiple x-intercepts, enter your answers as a comma-separated list.)
vertex
(x, y) = \left( -\frac{1}{2}, -\frac{33}{4} \right)
y-intercept
y = -8
x-intercepts
x = \frac{-1-\sqrt{33}}{2}, \frac{-1+\sqrt{33}}{2}
Since the graph is symmetric around the vertical line through the vertex, reflecting the y-intercept across the line of symmetry, we find the additional point (x, y) = () on the graph.
Determine the left-hand and right-hand behavior of the graph. (If an answer does not exist, enter DNE. If you need to use co or -co, enter INFINITY or -INFINITY, respectively.)
As the graph goes to the left without bound, the values of y approach
As the graph goes to the right without bound, the values of y approach
