The required function is [tex]y=-\frac{3}{4}(x-3)^2-7[/tex] , so the correct option is D.
Important information:
- Vertex = (3,-7)
- Other point = (1,-10)
Quadratic function:
The vertex form of a quadratic function is:
[tex]y=a(x-h)^2+k[/tex]
Where, [tex]a[/tex] is constant and [tex](h,k)[/tex] is vertex.
Substitute [tex]h=3,k=-7[/tex].
[tex]y=a(x-3)^2-7[/tex] ...(i)
Graph passes through the point (1, -10). Substitute [tex]x=1,y=-10[/tex] in (i).
[tex]-10=a(1-3)^2-7[/tex]
[tex]-10+7=4a[/tex]
[tex]-3=4a[/tex]
[tex]\dfrac{-3}{4}=a[/tex]
Substitute [tex]a=-\dfrac{3}{4}[/tex] in (i).
[tex]y=-\frac{3}{4}(x-3)^2-7[/tex]
Therefore, the correct option is D.
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