Answer:
You had set aside an evening to prepare yourself for an examination on the following
morning Your plans were disrupted when your aunt and uncle called in to visit
your parents who had gone to the theatre Narrate how you entertained the guests
and coped with your studies. Your composition should also bring out your feelings
on that evening
The required quadratic function for the given information is f(x)=3x²-12x-135.
Important information:
The x-intercepts of the quadratic function are (-5 0) and (9, 0). It means (x+5) and (x-9) are the two factors of the quadratic function.
[tex]f(x)=a(x+5)(x-9)[/tex] ...(i)
The graph of a quadratic function passes through (8, -39). So, substitute [tex]x=8,f(x)=-39[/tex] in (i).
[tex]-39=a(8+5)(8-9)[/tex]
[tex]-39=a(13)(-1)[/tex]
[tex]-39=-13a[/tex]
[tex]3=a[/tex]
Substitute [tex]a=3[/tex] in (i).
[tex]f(x)=3(x+5)(x-9)[/tex]
[tex]f(x)=3(x^2+5x-9x-45)[/tex]
[tex]f(x)=3(x^2-4x-45)[/tex]
[tex]f(x)=3x^2-12x-135[/tex]
Therefore, the required quadratic function is [tex]f(x)=3x^2-12x-135[/tex].
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