How do you find the intercept and vertex of y=(x+5)(x+3)?

1 Answer
Jul 26, 2017

Generally, how to find...
I. X-intercept(s)
- set y=0 and solve for x.
II. Y-intercept(s)
- set x=0 and solve for y.
III. Vertex
i. FOIL (distribute)
ii. vertex: (-b/2a, f(-b/2a))

For this question...
I. X-intercepts
y=(x+5)(x+3)
0=(x+5)(x+3)
x=5,3
x-intercepts: (-5,0), (-3,0)

II. Y-intercept
y=(x+5)(x+3)
y=(0+5)(0+3)
y=15
y-intercept: (0,15)

III. Vertex
y=(x+5)(x+3)
y=x2+8x+15
b2a=(8)2(1)=4
This is the x-value. To find the y-value plug in -4 for x and solve for y.
y=(4+5)(4+3)
y=-1
The vertex is (-4,-1)