How do you find the vertex and intercepts for #y=(x+3)(x+5)#?
1 Answer
y-intercept:
x-intercepts:
vertex:
Explanation:
Starting with the intercepts:
The y-intercept is the value of
#y# when#x=0# .
#y=(0+3)(0+5)=15# The x-intercept(s) is/are the values of
#x# when#y=0#
#0=(x+3)(x+5)#
#rArr x=-3# or#x=-5#
Determining the vertex.
Method 1:
For a parabola with a vertical axis,
the x coordinate of the vertex will be half way between the two x-intercepts.
i.e. the x-coordinate of the vertex will be#((-3)+(-5))/2 = -4#
By substituting#(-4)# for#x# in the given equation
#color(white)("XXX")y=(-4+3)(-4+5)=-1#
So the vertex will be at#(-4,-1)#
Method 2:
Convert the given equation into vertex form:
#y=m(x-color(red)(a))^2+color(green)(b)#
for a parabola with vertex at#(color(red)(a),color(green)(b))#
#color(white)("XXX")y=(x+3)(x+5)#
#color(white)("XXX")rarr y=x^2+8x+15#
#color(white)("XXX")rarr y=x^2+8xcolor(blue)(+16) + 15 color(blue)(-16)#
#color(white)("XXX")rarr y=(x+4)^2+(-1)#
#color(white)("XXX")rarr y = (x- (color(red)(-4)))^2+(color(green)(-1))#