Question

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function

Answer 1

B

given the equation of a parabola in standard form

y = ax² + bx + c : a ≠ 0

then the equation of the axis of symmetry which is also the x- coordinate of the vertex is obtained using

x = -
`(b)/(2a)`

y = 4x² + 5x - 1 is in standard form

with a = 4, b = 5 and c = - 1

`x_(vertex)` = -
`(5)/(8)`

hence axis of symmetry is x = -
`(5)/(8)`

to find the y-coordinate of the vertex substitute the x-coordinate into the equation

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

=
`(25)/(16)` -
`(50)/(16)` -
`(16)/(16)`

= -
`(41)/(16)` = - 2
`(9)/(16)`

vertex = ( -
`(5)/(8)`, - 2
`(9)/(16)`)