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PLEASE HELPA quadratic function has the form y=ax^2 + bx + c, in which a, b and c are specific numbers and a does not equal 0. Three distinct points on the graph are enough to determine the equation. Suppose that (1,5), (2,10) and (3,19) are on the graph of y =ax^2 + bx + c. Write a system of three variables and three equations.

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Problem

A quadratic function has the form y=ax^2 + bx + c, in which a, b and c are specific numbers and a does not equal 0. Three distinct points on the graph are enough to determine the equation. Suppose that (1,5), (2,10) and (3,19) are on the graph of y =ax^2 + bx + c. Write a system of three variables and three equations.​

Solution

For this case we can find the 3 equations on this way:

(x=1, y=5)

[tex]5=a(1)^2+b(1)+c=a+b+c[/tex]

(x=2, y=10)

[tex]10=a(2)^2+b(2)+c=4a+2b+c[/tex]

(x=3, y=19)

[tex]19=a(3)^2+b(3)+c=9a+3b+c[/tex]

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