A. H(x) = 4(x - 9)^2 - 17
B. H(x) = 4(x - 7)^2 - 19
C. H(x) = 4(x + 9)^2 - 17
D. H(x) = 4(x +7)^2 + 19
The answer is B. H(x) = 4(x - 7)^2 - 19
The equation which represents the transformation of [tex]H(x)=4x^2-16[/tex], will be [tex]H(x)=4(x+7)^2-19[/tex].
Transformation is the act or process of changing completely. In this also the graph changes or transform.
We have,
[tex]H(x)=4x^2-16[/tex]
And
It shifted [tex]7[/tex] units to the right and [tex]3[/tex] units down.
And the parent quadratic function is in the form of [tex]f(x)=a(x-h)^2+k[/tex]
Here,
"[tex]h[/tex]" tells if the vertex of the parabola is going left or right.
"[tex]k[/tex]" determines if the vertex of the parabola is going up or down.
So, According to the question;
We have,
[tex](a)[/tex] [tex]7[/tex] units to the right
[tex](b)[/tex] [tex]3[/tex] units down
So, Equation [tex]H(x)=4x^2-16[/tex] have moved the vertex of the parabola [tex]7[/tex] units to the right and [tex]3[/tex] units down.
Now,
[tex]f(x)=a(x-h)^2+k[/tex]
[tex]H(x)=4x^2-16[/tex]
Rewrite in the above form,
[tex]H(x)=4(x)^2-16[/tex]
Shifting right means adding [tex]7[/tex] i.e. [tex]h=7[/tex] and going down means subtracting [tex]3[/tex] i.e. [tex]k=3[/tex],
So,
[tex]H(x)=4(x)^2-16[/tex]
[tex]H(x)=4(x+7)^2-16-3[/tex]
[tex]H(x)=4(x+7)^2-19[/tex]
Hence, we can say that the equation which represents the transformation of [tex]H(x)=4x^2-16[/tex] , is given by [tex]H(x)=4(x+7)^2-19[/tex] .
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