SOLUTION: This is a three part question. The function b(x) is given below. b(x)≥ 1/4x^2 + x - 8 Part A.) Graph the inequality on a coordinate plane. Part B.) Explain how t

Algebra ->  Functions -> SOLUTION: This is a three part question. The function b(x) is given below. b(x)≥ 1/4x^2 + x - 8 Part A.) Graph the inequality on a coordinate plane. Part B.) Explain how t      Log On


   

Question 871247: This is a three part question.
The function b(x) is given below.
b(x)≥ 1/4x^2 + x - 8
Part A.) Graph the inequality on a coordinate plane.
Part B.) Explain how to decide which part to the graph to shade.
Part C.) How do you know if the boundary is included in the solution set?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The boundary, if exists, is ON the curve so would be included. Inequality given is of the inclusive kind, "... or equal to ...".

Notice how the statement is shown: b(x) IS GREATER THAN... You shade the region ABOVE and including the parabola.

You can transform the quadratic expression definition into standard form to help in graphing and in finding the roots. Complete the Square: %281%2F4%29%28x%5E2%2B4x%29-8
%281%2F4%29%28x%5E2%2B4x%2B4%29-8-1
highlight%28%281%2F4%29%28x%5E2%2B2%29%5E2-9%29

Vertex is (-2,-9); and you can find the roots if equate b(x)=0 and solve for x.