Graph y = x² - 6x + 9 (Perfect Square)
The parabola y = x² - 6x + 9 is a perfect square trinomial equal to (x-3)², with vertex at (3, 0).
How to use this tool
- Enter coefficient a (x²), coefficient b (x), constant c, x minimum and x maximum in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your vertex x and the full breakdown beneath it.
This perfect square trinomial factors as (x − 3)² and touches the x-axis at exactly one point, x = 3.
Frequently asked questions
- What does the discriminant tell me?
- If b²−4ac > 0 there are two real roots; = 0 one repeated root; < 0 no real roots (the parabola doesn't cross the x-axis).
- Does a affect the shape?
- Yes. a > 0 opens upward; a < 0 opens downward. Larger |a| makes it narrower.