Question

Look at the quadratic regression equation below to answer the following question: y = negative 2.096 x squared minus 2.25 x 9.038 for what value of x is y = negative 40? (use the quadratic formula to help solve the problem, x = startfraction negative b plus-or-minus startroot b squared minus 4 a c endroot over 2 a endfraction) a. x = 1.469, negative 2.543 b. x = 1.076, negative 5.403 c. x = 99.463, negative 100.536 d. x = 4.330, negative 5.403

Answer 1

To find the value of x when y equals negative 40 in the given quadratic equation, we can use the quadratic formula to solve for x. The solutions are approximately x ≈ 1.469 and x ≈ -2.543.

Step-by-step explanation:

To find the value of x when y equals negative 40, we can substitute y with -40 in the given quadratic equation, y = -2.096x^2 - 2.25x + 9.038, and solve for x using the quadratic formula.

Plugging in the values into the quadratic formula, we get:

x = (-(-2.25) ± √((-2.25)^2 - 4 * (-2.096) * (9.038 - 40))) / (2 * -2.096)

Simplifying the equation gives us:

x = (2.25 ± √(2.25^2 - 4 * (-2.096) * (-30.962))) / (-4.192)

Calculating the square root and simplifying further gives us two solutions for x:

x ≈ 1.469 or x ≈ -2.543