Question

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

Answer 1

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=x^2+8x+15`
`-b/(2a)=-((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)