Question

hours studied | exam grade
0 | 50
2 | 68
4 | 82
8 | 88
10 | 84
12 | 72
a.) write the equation for the model of best fit. you must upload a screenshot of desmos displaying your regression.
b.) estimate what the value of y will be when x=5. round your answer to the nearest tenth. upload your handwritten work displaying how you solved to receive credit.

Explanation:

Step1: Identify quadratic regression form

The quadratic model has the form $y = ax^2 + bx + c$, where $x$ = hours studied, $y$ = exam grade.

Step2: Input data to Desmos regression

Using the data points $(0,50), (2,68), (4,82), (8,88), (10,84), (12,72)$, run quadratic regression in Desmos. The resulting model is:
$y = -0.5x^2 + 9x + 50$

Step3: Substitute $x=5$ into the model

Calculate each term for $x=5$:

1. $-0.5(5)^2 = -0.5 \times 25 = -12.5$
2. $9(5) = 45$
3. Constant term: $50$

Sum the terms: $-12.5 + 45 + 50$

Step4: Compute final value for $x=5$

$ -12.5 + 45 + 50 = 82.5$

Answer:

a.) $y = -0.5x^2 + 9x + 50$ (verified via Desmos quadratic regression)
b.) $82.5$