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sleet_krkn [62]
3 years ago
15

Find the quadratic function that fits the following data. which one function fits.

Mathematics
1 answer:
Oksana_A [137]3 years ago
4 0

Answer:

C

Step-by-step explanation:

The general rule for the quadratic function is

y=ax^2+bx+c

Use the data from the table:

y(50)=130\Rightarrow 130=a\cdot 50^2+b\cdot 50+c\\ \\y(70)=130\Rightarrow 130=a\cdot 70^2+b\cdot 70+c\\ \\y(90)=200\Rightarrow 200=a\cdot 90^2+b\cdot 90+c

We get the system of three equations:

\left\{\begin{array}{l}2500a+50b+c=130\\ \\4900a+70b+c=130\\ \\8100a+90b+c=200\end{array}\right.

Subtract these equations:

\left\{\begin{array}{l}4900a+70b+c-2500a-50b-c=130-130\\ \\8100a+90b+c-2500a-50b-c=200-130\end{array}\right.\Rightarrow \left\{\begin{array}{l}2400a+20b=0\\ \\5600a+40b=70\end{array}\right.

From the first equation

b=-120a

Substitute it into the second equation:

5600a+40\cdot (-120a)=70\Rightarrow 800a=70,\\ \\ a=\dfrac{7}{80},\\ \\ b=-120\cdot \dfrac{7}{80}=-\dfrac{21}{2}=-10.5

So,

2500\cdot \dfrac{7}{80}+50\cdot (-10.5)+c=130\Rightarrow 218.75-525+c=130\\ \\c=130-218.75+525=436.25

The quadratic function is

y=\dfrac{7}{80}x^2-10.5x+436.25\\ \\y=0.0875x^2-10.5x+436.25

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