How do you find the vertex and intercepts for #y=2(x+1)(x-3)#?

1 Answer
Jun 9, 2018

#(1,-8),x=-1,x=3#

Explanation:

#"to find the intercepts set y = 0"#

#2(x+1)(x-3)=0#

#x+1=0rArrx=-1#

#x-3=0rArrx=3#

#"the vertex is on the axis of symmetry which is positioned"#
#"at the midpoint of the x-intercepts"#

#x_("vertex")=(-1+3)/2=1#

#"substitute this value into the equation for y"#

#y_("vertex")=2(2)(-2)=-8#

#color(magenta)"vertex "=(1,-8)#

#"for y-intercept set x = 0"#

#y=2(1)(-3)=-6#
graph{2(x+1)(x-3) [-16.02, 16.02, -8.01, 8.01]}