Question

Consider the following.

g(x) = 2x2 + 20x − 19; g(x) = 131
With the function indicate whether an input or output value is given.
g(x) = 131 . is an output value.
Calculate the corresponding output or input value. (Round your answers to three decimal places where appropriate. Enter your answers as a comma-separated list. Note: Even though the question may be completed without the use of technology, the authors intend for you to complete the activity using the technology you will be using in the remainder of the course so that you become familiar with the basic functions of that technology.)
x = -------

Answer 1

To find the input values for the function g(x) when the output is 131, set up the equation 2x^2 + 20x - 19 = 131 and solve for x using the quadratic formula, factoring, or graphing, rounding the solutions to three decimal places.

Step-by-step explanation:

Given the quadratic function g(x) = 2x2 + 20x - 19, and knowing that g(x) = 131, we need to find the value(s) of x that correspond to this output value. The equation representing our situation is:

2x2 + 20x - 19 = 131.

To solve for x, we first move all terms to one side of the equation:

2x2 + 20x - 150 = 0.

You can use the quadratic formula, graphing, or factoring to find the roots of this equation. However, it is not factorable with integer roots, so the quadratic formula or graphing are likely more appropriate here.

After applying the quadratic formula, x would have two possible values, which should be rounded to three decimal places, as requested.