# How many intercepts does #y = x^2 − 6x + 9# have?

##### 1 Answer

One

#### Explanation:

You can determine **zero** and

When

#x^2 - 6x + 9 = 0#

In order to determine how many solutions this quadratic equation has, you can calculate the value of its **discriminant**,

For a quadratic equation that takes the general form

#color(blue)(ax^2 + bx + c = 0)#

the discriminant is equal to

#color(blue)(Delta = b^2 - 4ac)#

In your case, you have

#Delta = (-6)^2 - 4 * 1 * 9#

#Delta = 36 - 36 = color(green)(0)#

When the discriminant is equal to **zero**, your equation will only have **one real solution** (a repeated root) that takes the form

#x = (-b +- sqrt(Delta))/(2a) = (-b +- 0)/(2a) = -b/(2a)#

In your case, the root will be

#x = -((-6))/(2 * 1) = 6/2 = 3#

This means that the function has **one**

The

#y = (0)^2 - 6 * (0) + 9 = 9#

The function will thus intercept the

graph{x^2 - 6x + 9 [-10, 10, -5, 5]}