# How do you find the vertex and intercepts for #y = x^2 - 4x + 3#?

##### 1 Answer

Dec 21, 2015

vertex at

y-intercept:

x-intercepts:

#### Explanation:

To find the vertex rewrite the given equation

into vertex form:

Complete the square

#color(white)("XXX")y=x^2-4xcolor(blue)(+2^2)+3color(blue)(-4)#

Rewrite as a squared binomial and simplified constant (in vertex form)

#color(white)("XXX")y=1(x-2)^2+(-1)#

with vertex at#(2,-1)#

The y-intercept is the value of

For

#y=x^2-4x+3# when#x=0#

#color(white)("XXX")y=9^2-4xx(0)+3 = 3#

The x-intercepts are the values when

Since

#y=x^2-4x+3#

can be factored as#y=(x-3)(x-1)#

when#y=0#

#color(white)("XXX")x=3# or#x=1#