Question

solve the equation by graphing the related function.
$x^2 - 9x = 0$
graph the related function. choose the correct graph below.
oa.
graph a
ob.
graph b
oc.
graph c
od.
graph d
help me solve this view an example get more help

Explanation:

Step1: Define related function

The related function of $x^2 - 9x = 0$ is $y = x^2 - 9x$.

Step2: Find x-intercepts

Set $y=0$, solve $x^2 - 9x = 0$. Factor: $x(x-9)=0$. So $x=0$ or $x=9$. The graph crosses x-axis at $(0,0)$ and $(9,0)$.

Step3: Find vertex of parabola

For $y=ax^2+bx+c$, vertex x-coordinate is $x=-\frac{b}{2a}$. Here $a=1$, $b=-9$, so $x=\frac{9}{2}=4.5$. Substitute $x=4.5$ into function: $y=(4.5)^2 - 9(4.5)=20.25 - 40.5=-20.25$. Vertex is $(4.5, -20.25)$.

Step4: Match to correct graph

The parabola opens upward (since $a=1>0$), has x-intercepts at 0 and 9, and a vertex below the x-axis. This matches Graph A.

Answer:

A. <The graph with upward-opening parabola crossing x-axis at 0 and 9, vertex in the fourth quadrant>