Question

Determine the vertex
5) 7n^2- 40n + 25 = 0

How do I get the vertex?

Answer 1

vertex = (
`(20)/(7)`, -
`(225)/(7)` )

Explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

Then the x- coordinate of the vertex is

`x_(vertex)` = -
`(b)/(2a)`

7n² - 40n + 25 = 0 ← is in standard form

with a = 7, b= - 40 , thus

`x_(vertex)` = -
`(-40)/(14)` =
`(20)/(7)`

Substitute this value into the equation for corresponding y- coordinate

7(
`(20)/(7)` )² - 40(
`(20)/(7)` ) + 25

= 7(
`(400)/(49)` ) -
`(800)/(7)` + 25

=
`(400)/(7)` -
`(800)/(7)` + 25

= -
`(400)/(7)` +
`(175)/(7)` = -
`(225)/(7)`

vertex = (
`(20)/(7)`, -
`(225)/(7)` )