Question

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y = 4x^2 + 5x – 1.

Answer 1

The equation of the axis of symmetry is x =
`-(5)/(8)`

The coordinates of the vertex are (
`-(5)/(8)` ,
`-2(9)/(16)` ) ⇒ 2nd answer

Explanation:

The quadratic function y = ax² + bx + c is represented graphically by a parabola which has a minimum/maximum vertex (h , k), where

• h =
  `-(b)/(2a)` and k is value y at x = h
• The axis of symmetry of the parabola is a vertical line passes through the vertex point and its equation is x = h
• The minimum/maximum value of the function is (h , k)

∵ y = 4x² + 5x - 1

∵ The form of the quadratic function is y = ax² + bx + c

∴ a = 4 , b = 5 , c = -1

∵ The coordinates of the vertex points are (h , k)

∵ h =
`-(b)/(2a)`

∴ h =
`-(5)/((2)(4))=-(5)/(8)`

- To find k substitute x in the function by
`-(5)/(8)`

∵ k = 4 (
`-(5)/(8)` )² + 5(
`-(5)/(8)` ) - 1

∴ k = 4 (
`(25)/(64)` ) + (
`-(25)/(8)` ) - 1

∴ k =
`(25)/(16)` -
`(25)/(8)` - 1

∴ k =
`-2(9)/(16)`

∴ The coordinates of the vertex are (
`-(5)/(8)` ,
`-2(9)/(16)` )

∵ The equation of the axis of symmetry is x = h

∵ h =
`-(5)/(8)`

∴ The equation of the axis of symmetry is x =
`-(5)/(8)`