# quadratic equation and inequality

1) What is the meaning and purpose of the axis of a quadratic function?

2) Solve the inequalities. State the solution set using interval notation for:

(x - 4) / (x + 3) < 0

and then for:

(x - 4) / (x + 3) > 0

What do you get when uniting the two sets of solutions?

3) The surface area A, of a cylinder with height h, and radius r, is given by the equation A = 2prh + 2pr^2. Find the radius of a cylinder with height 2 cm and area 4p cm2.

4) An arrow is shot straight upward with a velocity of 96 feet per second at instant t0 = 0; its altitude is defined in time by the following function:

f(t) = -16t² + 96t + 6.

From what altitude is it shot? For how many seconds is this arrow more than 86 feet high?

https://brainmass.com/math/basic-algebra/quadratic-equation-inequality-108140

#### Solution Preview

Please see the attached file for detailed solutions.

) What is the meaning and purpose of the axis of a quadratic function?

For a quadratic function of , it can also be written as

Then line of axis is , this is also the symmetric line of the graph of this quadratic function.

When you graph the curve, you can just draw the left or right side of the , then the other half can be obtained by the symmetry.

Another use of axis of the quadratic function is the ...

#### Solution Summary

The solution explains the meaning of the line of axis of a quadratic equation. It also explains how to solve a complex inequality. Finally, it finds the height of the arrow when it is shot straight upward.