Question

question 1 what is the quadratic regression equation for the data set? y -0.175x² - 3.786x + 121.119 y -0.175(3.786)x y -0.175x - 3.786 y -0.175x² + 3.786x + 121.119 x y 6 100 3 110 10 50 3 90 5 120 15 30 9 70 1 pts

Explanation:

Step1: Recall quadratic regression formula

The general form of a quadratic regression equation is $y = ax^{2}+bx + c$. To find the values of $a$, $b$, and $c$ for a given data - set, we can use statistical software or a calculator with regression capabilities. Since we are given options, we can substitute the $x$ - values from the data - set into each equation and check which one gives the closest $y$ - values.
Let's take the first option $y=-0.175x^{2}-3.786x + 121.119$.
For $x = 6$:
$y=-0.175\times6^{2}-3.786\times6 + 121.119$
$y=-0.175\times36-22.716 + 121.119$
$y=-6.3-22.716 + 121.119$
$y=92.103$ (close to 100)
For $x = 3$:
$y=-0.175\times3^{2}-3.786\times3 + 121.119$
$y=-0.175\times9-11.358 + 121.119$
$y=-1.575-11.358 + 121.119$
$y=108.186$ (close to 110)
We can continue this process for other data - points in the set.

Step2: Analyze other options

The second option $y=-0.175(3.786)x$ is a linear function, not a quadratic function. The third option $y=-0.175x-3.786$ is also a linear function.
The fourth option $y=-0.175x^{2}+3.786x + 121.119$:
For $x = 6$:
$y=-0.175\times6^{2}+3.786\times6 + 121.119$
$y=-0.175\times36 + 22.716+121.119$
$y=-6.3 + 22.716+121.119$
$y=137.535$ (not close to 100)

Answer:

$y=-0.175x^{2}-3.786x + 121.119$