Question

1. Find the vertex of the graphs of the following quadratic equations.

a. y = 2(x − 5)^2 + 3.5
b. y = −(x + 1)^2 − 8

Answer 1

a) Vertex:
`(h,k) = (5,3.5)`

b) Vertex:
`(h,k) = (-1,-8)`

Explanation:

First we need to realize that these equations are the equations of parabolas.

the equation of parabola are generally written as:

`y = a(x-h)^2 +k`

where the vertex is the point
`(h,k)`. (note that the sign of 'h' is changed!)

(also note that the value of 'a' doesn't matter for finding vertex point)

given this information we can now easily find out the vertex of both parabolas

a)
`y = 2(x-5)^2 + 3.5`

by comparing it with the general equation above, we can see that -5 is in the place of '-h' and +3.5 is in the place of '+k'

we can write

`-h = -5` and solve for h.

`h=5`

similarly,

`k=3.5`

hence the vertex of this graph is
`(h,k) = (5,3.5)`

b)
`y=-(x + 1)^2-8`

by comparing it with the general equation above, we can see that +1 is in the place of '-h' and -8 is in the place of '+k'

we can write

`-h = +1` and solve for h.

`h = -1`

similarly,

`k=-8`

hence the vertex of this graph is
`(h,k) = (-1,-8)`