Question

question 16 of 25
what is the quadratic regression equation that fits these data?
number of seconds | height (in feet)
0 | 12
1 | 13
2 | 15
3 | 13
4 | 9
5 | 7
a. $y=14.77(0.89^{x})$
b. $y=-2.04x^{2}+1.46x+13.92$
c. $y=-0.70x^{2}+2.37x+11.96$
d. $y=-1.04x^{2}+3.04x+9.68$

Explanation:

Step1: Test x=0 in each option

For A: $y=14.77(0.89^0)=14.77$, does not match 12.
For B: $y=-2.04(0)^2+1.46(0)+13.92=13.92$, does not match 12.
For C: $y=-0.70(0)^2+2.37(0)+11.96=11.96\approx12$, matches.
For D: $y=-1.04(0)^2+3.04(0)+9.68=9.68$, does not match 12.

Step2: Verify x=1 for option C

$y=-0.70(1)^2+2.37(1)+11.96=-0.70+2.37+11.96=13.63\approx13$, matches.

Step3: Verify x=2 for option C

$y=-0.70(2)^2+2.37(2)+11.96=-2.8+4.74+11.96=13.9\approx15$ (close, and closer than others).

Step4: Verify x=3 for option C

$y=-0.70(3)^2+2.37(3)+11.96=-6.3+7.11+11.96=12.77\approx13$, matches.

Step5: Verify x=4 for option C

$y=-0.70(4)^2+2.37(4)+11.96=-11.2+9.48+11.96=10.24\approx9$, close match.

Step6: Verify x=5 for option C

$y=-0.70(5)^2+2.37(5)+11.96=-17.5+11.85+11.96=6.31\approx7$, close match.

Answer:

C. $y=-0.70x^{2}+2.37x+11.96$