Question

Without graphing, state the vertex for each of the following quadratic equations.

a. y = (x − 5)^2 + 3
b. y = x^2 − 2.5
c. y = (x + 4)^2

Answer 1

`(5,3)`

`(0,-2.5)`

`(-4,0)`

Explanation:

The equation of a parabola in the form of the vertex is the following:

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

and the vertex will be in the coordinates:
`(h,k)`

for a.
`y = (x - 5)^2 + 3`

we can see that
`h=5`, and
`k=3`

so the vertex is at
`(5,3)`

for b.
`y =x^2 - 2.5`

we can re accommodate this equation as:
`y=(x-0)^2+(-2.5)`

in this form is easier to see that
`h=0`, and
`k=-2.5`

so the vertex is at
`(0,-2.5)`

for c.
`y = (x + 4)^2`

we can re accommodate this equation as:
`(x-(-4))^2+0`

and as we can see
`h=-4` and
`k=0`

so the vertex is at
`(-4,0)`