1. Transform the following equations to canonical forms a) \( x^{2}+4 x y+4 y^{2}-20 x+10 y-50=0 \) b) \( 3 x^{2}+10 x y+3 y^{2}-12 x-12 y+4=0 \) c) \( x^{2}+2 x y+y^{2}-4 x-4 y+3=0 \) d) \( 9 x^{2}+24 x y+16 y^{2}-126 x+82 y-59=0 \) e) \( 3 x^{2}-8 x y-3 y^{2}+10 x-13 y+8=0 \) f) \( 3 x^{2}-5 x y+6 y^{2}+11 x-17 y+13=0 \) g) \( 9 x^{2}+24 x y+16 y^{2}+34 x+62 y+47=0 \) h) \( x^{2}-4 x y+4 y^{2}-12 x-6 y-39=0 \)

122. Постройте график функции \( y=-x^{2}+2 x+8 \) и найдите, ис- пользуя график: а) значение функции при \( x=2,5 ;-0,5 ;-3 ; \) б) значения аргумента, при которых \( y=6 ; 0 ;-2 \); в) нули функции и промежутки знакопостоянства; г) промежутки возрастания и убывания функции, область зна- чений функции.

Clearly indicate all intercepts with the axes as well as the QUESTION 7 Given the function with the equation \( k(x)=\frac{-6}{x+2}-2 \) : 7.1 Write the equations of the asymptotes of \( k \). 7.2 Give the range of \( k \). 7.3 Give the domain of \( k \).

(a) Express the distance \( d \) from \( P \) to the origin as a function of \( x \). \( d(x)=\sqrt{x^{4}-3 x^{2}+4} \) (Simplify your answer. Type an exact answer, using radicals as needed.) (b) What is \( d \) if \( x=0 \) ? If \( x=0 \), the distance \( d \) is 2 . (Type an integer or decimal rounded to two decimal placels as needed.) (c) What is \( d \) if \( x=1 \) ? If \( x=1 \), the distance \( d \) is \( \square \). (Type an integer or decimal rounded to two decimal places as needed.)

Given the function with the equation \( k(x)=\frac{-6}{x+2}-2 \) : \( 7.1 \quad \) Write the equations of the asymptotes of \( k \).

QUESTION 7 Given the function with the equation \( k(x)=\frac{-6}{x+2}-2 \) : \( 7.1 \quad \) Write the equations of the asymptotes of \( k \).