EvangelynP435356 EvangelynP435356

30-10-2022
Mathematics

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Write a quadratic function whose graph has x intercepts of 7 and 10 and passes through (2,4) what is the value of Y

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PrimroseZ732983 PrimroseZ732983

30-10-2022

A quadratic function with x-intercepts 7 and 10 has the form (because when x = 10 , y = 0 and x = 7, y = 0)

[tex]y=c(x-10)(x-7)[/tex]

where c is a constant hitherto unknown.

We are told that the quadratic function passes through (2, 4) meaning when x = 2 then y = 4. Putting these values into the above equation gives us

[tex]4=c(2-10)(2-7)[/tex]

[tex]\rightarrow4=40c[/tex][tex]\therefore c=0.1[/tex]

Hence, the final form of our quadratic equation is

[tex]y=0.1(x-10)(x-7)[/tex]

which is our answer.

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