Answer:
The resulting equation in the vertex form is [tex](y-4)=-(x-4)^2[/tex] having the vertex at the point (4,4).
Step-by-step explanation:
The given function is f(x) = -x² + 8x-7.
As the given function is translated 5 units down, so, subtract 5 units in the given function.
The resulting function, y = f(x) -5
[tex]\Rightarrow y= - x² + 8x - 7 - 5 \\\\\Rightarrow y = - x² + 8x - 12[/tex]
Now converting the obtained equation to vertex form,
[tex]y= - x² + 8x - 12 \\\\\Rightarrow y = -(x^2-8x+12) \\\\[/tex]
Adding and subtraction 4 as
[tex]y= -(x^2-8x+12+4-4) \\\\\Rightarrow y= -(x^2-8x+16-4) \\\\\Rightarrow y= -((x-4)^2-4) \\\\\Rightarrow (y-4)=-(x-4)^2[/tex]
The vertex of the above equation is (4,4).
Hence, on translating five units in the downwards direction, the resulting equation in the vertex form is [tex](y-4)=-(x-4)^2[/tex] having the vertex at the point (4,4).
