Question

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y = 4x2 + 5x – 1.

Answer 1

(
`-(5)/(8)` ,
`- (41)/(6)`
x=
`-(5)/(8)`

Answer 2

Answer: The equation of the axis of symmetry is
`x=-(5)/(8)` and the co-ordinates of the vertex are
`\left(-(5)/(8),-(41)/(16)\right).`

Step-by-step explanation: We are given to find the axis of symmetry and the coordinates of the vertex of the graph of the following function:

`y=4x^2+5x-1~~~~~~~~~~~~~~~~~~~~~~~~(i)`

The given equation (i) describes a parabola.

The standard equation of a parabola in vertex form is given by

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

where the co-ordinates of the vertex are (h, k) and the equation of axis of symmetry is

`x=h.`

From equation (i), we have

`y=4x^2+5x-1\\\\\Rightarrow y=4\left(x^2+(5)/(4)x\right)-1\\\\\\\Rightarrow y=4\left(x^2+(5)/(4)x+(25)/(64)\right)-1-(25)/(16)\\\\\\\Rightarrow y=\left(x+(5)/(8)\right)^2-(41)/(16).`

Comparing with the vertex form, we get

`(h,k)=\left(-(5)/(8),-(41)/(16)\right)`

and the equation of axis of symmetry is

`x=-(5)/(8).`

Thus, the equation of the axis of symmetry is
`x=-(5)/(8)` and the co-ordinates of the vertex are
`\left(-(5)/(8),-(41)/(16)\right).`