Question

Label the vertex of this function
`y=-3(x-1)(x+4)`:

Answer 1

vertex = ( -
`(3)/(2)`,
`(75)/(4)` )

Explanation:

Given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

Then the x- coordinate of the vertex is

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

Given

y = - 3(x - 1)(x + 4) ← expand the factors using FOIL

= - 3(x² + 3x - 4) ← distribute parenthesis by - 3

= - 3x² - 9x + 12 ← in standard form

with a = - 3 and b = - 9 , thus

`x_(vertex)` = -
`(-9)/(-6)` = -
`(3)/(2)`

Substitute this value into the equation for corresponding value of y

y = - 3( -
`(3)/(2)` - 1)( -
`(3)/(2)` + 4)

= - 3 × -
`(5)/(2)` ×
`(5)/(2)`

= - 3 × -
`(25)/(4)`

=
`(75)/(4)`

Thus

vertex = ( -
`(3)/(2)`,
`(75)/(4)` )