Question

Help me pls kinda stuck lol

Answer 1

see explanation

Explanation:

(a)

To find the x- intercepts , let y = 0 , that is

6x - x² = 0 ← factor out x from each term

x(6 - x) = 0

Equate each factor to zero and solve for x

x = 0

6 - x = 0 ⇒ x = 6

Coordinates of P (6, 0 )

(b)

The axis of symmetry is a vertical line, positioned at the midpoint of the zeros

x =
`(0+6)/(2)` =
`(6)/(2)` = 3

Equation of axis of symmetry is x = 3

(c)

Given a parabola in standard form y = ax² + bx + c ( a ≠ 0 )

Then the x- coordinate of the vertex is

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

y = 6x - x² = - x² + 6x ← is in standard form

with a = - 1, b = 6 , then

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

Substitute x = 3 into y = 6x - x² for y- coordinate

y = 6(3) - 3² = 18 - 9 = 9

coordinates of maximum point = (3, 9 )