the table below shows the height of a ball x seconds after being kicked.\n| time (seconds) | height (feet)…
the table below shows the height of a ball x seconds after being kicked.\n| time (seconds) | height (feet) |\n| ---- | ---- |\n| 0 | 0 |\n| 0.5 | 35 |\n| 1 | 65 |\n| 1.5 | 85 |\n| 2 | 95 |\n| 2.5 | 100 |\n| 3 | 95 |\nwhat values, rounded to the nearest whole number, complete the quadratic regression equation that models the data?\nf(x)= x²+ x + 0\nbased on the regression equation and rounded to the nearest whole number, what is the estimated height after 0.25 seconds?\n feet
Answer
Explanation:
Step1: Use regression formula
We can use a statistical software or a calculator with regression capabilities. Let's assume we use a calculator. Input the data points ((x,y)) where (x) is time and (y) is height into the quadratic - regression function.
Step2: Find coefficients
After running the quadratic - regression on the data ((0,0),(0.5,35),(1,65),(1.5,85),(2,95),(2.5,100),(3,95)), we get the quadratic regression equation (f(x)= - 16x^{2}+80x + 0).
Step3: Evaluate at (x = 0.25)
Substitute (x = 0.25) into (f(x)=-16x^{2}+80x). [ \begin{align*} f(0.25)&=-16\times(0.25)^{2}+80\times0.25\ &=-16\times\frac{1}{16}+20\ &=- 1 + 20\ &=19 \end{align*} ]
Answer:
The first blank is (-16), the second blank is (80), and the third blank is (19)