Find the Equation of the Parabola Passing Through the Given $( - 2,6 ) , ( 1,12 )$

question 22

Multiple Choice

Find the equation of the parabola passing through the given points. $( - 2,6 ) , ( 1,12 )$ , and $( 2,18 )$

• A) \(\quad y = - 2 x ^ { 2 } + 3 x + 20\)
• B) \(y = x ^ { 2 } + 3 x + 8\)
• C) \(y = 3 x + 3\)
• D) \(\quad y = x ^ { 2 } - 3 x + 8\)
• E) none of these

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Definitions:

Manipulating Factors

Variables that are deliberately changed or manipulated in an experiment to observe their effect on other variables.

Experiments

Research methods involving the manipulation of one or more variables to determine their effects on a dependent variable, allowing for the establishment of cause-and-effect relationships.

Random Sampling

A technique for selecting a sample from a population in a way that every individual has an equal chance of being chosen.

Random Assignment

A method used in experiments to place participants into different groups in a way that every individual has an equal chance of being assigned to any group, ensuring the fairness and validity of the research.