Which quadratic function in vertex form can be represented by the graph that has a vertex at (3, -7) and passes through the point (1, -10)?
I really need the answer QUICK please​

Answer:

Answer is D

Step-by-step explanation:

(3,-7) and (1,-10) belong toD Variant

The required function is [tex]y=-\frac{3}{4}(x-3)^2-7[/tex] , so the correct option is D.

Important information:

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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