Question

100 POINTS !!! Find the axis of symmetry and the vertex of the graph of y = 6x2 − 24x + 11. x = 2; (2, −13) x = 4; (4, 11) x = −2; (−2, 83) x = −4; (−4, −11)

Answer 1

Let's see

`\\ \rm\rightarrowtail y=6x^2-25x+11`

Graph attached

• vertex(-2,-13)

Axis of symmetry

• x=-2

Answer 2

axis of symmetry: x = 2

vertex: (-2, 13)

Explanation:

Given function

`\sf y=6x^2-24x+11`

Vertex form

`\sf y=a(x-h)^2+k`
where (h, k) is the vertex

Expand vertex form:

`\sf \implies y=ax^2-2ahx+ah^2+k`

Compare coefficients of expanded vertex form with given function:

coefficient of
`\sf x^2`:

⇒ a = 6

coefficient of
`\sf x`:

⇒ -2ah = -24

⇒ ah = 12

⇒ 6h = 12

⇒ h = 2

constant:

⇒
`\sf ah^2+k=11`

⇒
`\sf 6 \cdot 2^2+k=11`

⇒
`\sf 24+k=11`

⇒
`\sf k=-13`

Vertex

Vertex = (2, -13)

Axis of symmetry

Axis of symmetry is when x = h

Therefore, axis of symmetry is x = 2