Match the graph with its function using the x-intercepts.
-$y = \left( x ^ { 2 } - 2 x \right) ^ { 2 } - 18 \left( x ^ { 2 } - 2 x \right)$ and $y = - 45$
A) $= 3 , - 1,5,3$
B) 15,3
C) 5,3
D) $- 3 , - 1,15,3,5,3$

Question

Quizplus · Accepted Answer

The given function can be simplified by setting $z = x^2 - 2x$, resulting in $y = z^2 - 18z$. Factoring, we get $y = z(z - 18)$, which implies $z = 0$ or $z = 18$. Substituting back for $x$, we have $x^2 - 2x = 0$ and $x^2 - 2x = 18$. Solving these equations gives the x-intercepts at $x = 0, 2, -3$, and $5$. The constant function $y = -45$ does not have x-intercepts, so it doesn't match with any of the given options.

Match the Graph with Its Function Using the X-Intercepts y=(x2−2x)2−18(x2−2x)y = \left( x ^ { 2 } - 2 x \right) ^ { 2 } - 18 \left( x ^ { 2 } - 2 x \right)y=(x2−2x)2−18(x2−2x)

Match the Graph with Its Function Using the X-Intercepts $y = \left( x ^ { 2 } - 2 x \right) ^ { 2 } - 18 \left( x ^ { 2 } - 2 x \right)$