How do you find the vertex and intercepts for #g(x) = x^2 - 4x + 2#?

1 Answer
Jan 1, 2016

#color(blue)("Vertex " -> (x,y)-> (2, -2)#;
#ycolor(white)(.)_("intercept")=2#

#xcolor(white)(.)_("intercpts") -> # I have taken you to the point where all you have to do is the final arithmetic

Explanation:

Given: #g(x)=x^2-4x+2#
Tony B

The quick way for some of it!
There is no coefficient in front of #x^2# so we can use:

Consider the coefficient of #(-4)# from #-4x#
#color(brown)(x_("vertex") = (-1/2)(-4) = +2)#

so by substitution:

#color(brown)(y_("vertex") =(2)^2-4(2)+2 = -2)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The #y_("intercept") # is at #x=0#

#color(brown)(=> y_("intercept") = (0)^2-4(0)+2 = 2)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Not so quick to find the values for #x_("intercept")# as its factors are non integer values.

Consider standard equation form of: #ax^2+bx+c=0#

and the related #x=(-b+-sqrt(b^2-4ac))/(2a)#

giving: #x=(-(-4) +-sqrt((-4)^2-4(1)(2)))/(2(1))#

#color(green)("I will let you solve that part. Compare your answers to the graph.")#