# How many intercepts does #y = x^2 − 5x + 6# have?

##### 1 Answer

#### Answer:

Two

#### Explanation:

You can find this function's **zero** and its

For the

#x^2 - 5x + 6 = 0#

You can determine how many solutions this quadratic has by calculating its **discriminant**,

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

takes the form

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

In your case, the discriminant will be

#Delta = (-5)^2 - 4 * 1 * 6#

#Delta = 25 - 24 = color(green)(1)#

When *two distinct real roots* that take the form

#color(blue)(x_(1,2) = (-b +- sqrt(Delta))/(2a))#

In your case, these roots will be

#x_(1,2) = (-(-5) +- sqrt(1))/(2 * 1)#

#x_(1,2) = (5 +- 1)/2 = {(x_1 = (5 + 1)/2 = 3), (x_2 = (5-1)/2 = 2) :}#

This means that the function will have two

The

#y = (0)^2 - 5 * (0) + 6 = 6#

The function will intercept the

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