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loris [4]
3 years ago
8

1. Write a quadratic function, in standard form, that fits the set of points. Solve it as a system of three equations

Mathematics
1 answer:
sasho [114]3 years ago
5 0

Answer:

The equation is y=2x^2+4x-7

Step-by-step explanation:

Let the quadratic function be


y=ax^2+bx+c


The point (-4,9) must satisfy this function,

\Rightarrow a(-4)^2+b(-4)+c=9


\Rightarrow 16a-4b+c=9...(1)


The point (0,-7) must also satisfy this function,

\Rightarrow a(0)^2+b(0)+c=-7


\Rightarrow c=-7...(2)



The point (1,-1) must also satisfy this function,

\Rightarrow a(1)^2+b(1)+c=-1


\Rightarrow a+b+c=-1...(3)


We put equation 2 into equation 1 to get;


\Rightarrow 16a-4b-7=9


\Rightarrow 16a-4b=16


\Rightarrow 4a-b=4...(5)


We again put equation 2 into equation 3 to get;


\Rightarrow a+b-7=-1


\Rightarrow a+b=6...(6)


We add equation 5 and 6 to get;

5a=10


\Rightarrow a=2


We put a=2 into equation 6 to get;


2+b=6


\Rightarrow b=6-2


\Rightarrow b=4


The equation is therefore y=2x^2+4x-7

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