Answer:
[tex]x=\frac{3}{2}[/tex]
Step-by-step explanation:
If you are asking what type of geometric figure this equation forms, it is a parabola. I am assuming you want to solve for x. If that is the case, here is your solution.
Given: [tex]y=4x^2-12x+9[/tex]
To solve for the x value, we set y equal to 0. To save some time, we can use the quadratic formula to solve this equation - since it is a quadratic. The formula is:
[tex]x=\frac{-b+\sqrt{b^2-4ac}}{2a}[/tex] and [tex]x=\frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]
Let's identify our values:
[tex]a=4\\b=-12\\c=9[/tex]
To solve for x, we need to plug this into the quadratic formula.
[tex]x=\frac{12+\sqrt{(-12)^2-4(4)(9)}}{2(4)}[/tex]
[tex]x=\frac{12+\sqrt{0}}{8}[/tex]
[tex]x=\frac{12+0}{8}[/tex]
[tex]x=\frac{12}{8}[/tex]
[tex]x=\frac{3}{2}[/tex]
We would normally do the process again, but subtracting. However, since it was plus/minus zero, the answer would not change. You get one real solution.
