The scatterplot above shows the avrage therms of naturela gas used by residential constomeers over a 12-month period. Of the following equations, which best models the data in the scatterplot ?
A
`y =1.061^(x)+ 312.9`
B
`y=-1.061^(x)-312.9`
C
`y=6.1x ^(2)-85.1x+312.9`
D
`y =- 6.1 x ^(21) + 85. 1 x - 312.9`
Text Solution
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The correct Answer is:
C
The data in the scatterplot can be modeled by a parabola opening upwars. (A) is an exponential growth equation, and (B) is an exponential decay equation. Neither will graph as a parabola, so eliminate both. Recall that a parabola is the graph of a quadratic. For a quadratic equation in the form `ax ^(2) +bx+c,a` determines whether the parabola opens upward of downward and c is teh y-intercept. When `a gt 0,` the parabola opens upward, so (C ) is correct. (D) is a quadratic equation, but `a lt 0,` so this equation would graph as a parabola that opens downeard.
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