Q:

How many points does the given equation have in common with the x-axis and where is the vertex in relation to the x-axis. y=x^2-12x+12

Accepted Solution

A:
Answer: 1. It has two points in common with the x-axis. 2. The vertex in relation to the x-axis is at [tex]x=6[/tex]Step-by-step explanation: The points that the equation has in common with the x-axis are the points of intersection of the parabola with the x-axis. To find them, substitute y=0 and solve for "x": [tex]y=x^2-12x+12\\0=x^2-12x+12[/tex] Use the Quadratic formula: [tex]x=\frac{-b\Β±\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-(-12)\Β±\sqrt{(-12)^2-4(1)(12)}}{2(1)}\\\\x_1=10.89\\\\x_2=1.10[/tex] It has two points in common with the x-axis. To find the vertex in relation to the x-axis, use the formula: [tex]x=\frac{-b}{2a}[/tex] Substituting values, you get: [tex]x=\frac{-(-12)}{2(1)}\\x=6[/tex]