Match the graph with its function using the x-intercepts.
-$y = \left( x - \frac { 10 } { x } \right) ^ { 2 } - 6 \left( x - \frac { 10 } { x } \right)$ and $y = 27$
A) $- 5 , - 1,2,10$
B) $- 3,9$
C) $- 5,2$
D) No solution

Question

Quizplus · Accepted Answer

The given function can be simplified by setting $y = \left( x - \frac { 10 } { x } \right) ^ { 2 } - 6 \left( x - \frac { 10 } { x } \right)$ equal to 0 to find its x-intercepts. Let $z = x - \frac{10}{x}$, then the equation becomes $z^2 - 6z = 0$, which factors to $z(z - 6) = 0$, giving $z = 0$ or $z = 6$. Substituting back for $z$, we get $x - \frac{10}{x} = 0$ and $x - \frac{10}{x} = 6$. Solving these equations gives the x-intercepts as $-5, -1, 2,$ and $10$.

Match the Graph with Its Function Using the X-Intercepts y=(x−10x)2−6(x−10x)y = \left( x - \frac { 10 } { x } \right) ^ { 2 } - 6 \left( x - \frac { 10 } { x } \right)y=(x−x10​)2−6(x−x10​)

Match the Graph with Its Function Using the X-Intercepts $y = \left( x - \frac { 10 } { x } \right) ^ { 2 } - 6 \left( x - \frac { 10 } { x } \right)$