Question

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

Answer 1

Answer:

1. It has two points in common with the x-axis.

2. The vertex in relation to the x-axis is at $x=6$

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":

$y=x^2-12x+12\\0=x^2-12x+12$

Use the Quadratic formula:

$x=\frac{-b\±\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-(-12)\±\sqrt{(-12)^2-4(1)(12)}}{2(1)}\\\\x_1=10.89\\\\x_2=1.10$

It has two points in common with the x-axis.

To find the vertex in relation to the x-axis, use the formula:

$x=\frac{-b}{2a}$

Substituting values, you get:

$x=\frac{-(-12)}{2(1)}\\x=6$