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Sagot :
Given:
The vertex of a quadratic function is (4,-7).
To find:
The equation of the quadratic function.
Solution:
The vertex form of a quadratic function is:
[tex]y=a(x-h)^2+k[/tex] ...(i)
Where a is a constant and (h,k) is vertex.
The vertex is at point (4,-7).
Putting h=4 and k=-7 in (i), we get
[tex]y=a(x-4)^2+(-7)[/tex]
[tex]y=a(x-4)^2-7[/tex]
The required equation of the quadratic function is [tex]y=a(x-4)^2-7[/tex] where, a is a constant.
Putting a=1, we get
[tex]y=(1)(x-4)^2-7[/tex]
[tex]y=(x^2-8x+16)-7[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
[tex]y=x^2-8x+9[/tex]
Therefore, the required quadratic function is [tex]y=x^2-8x+9[/tex].
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