Question

Consider the quadratic function:

f(x) = x2 – 8x – 9



Vertex: (StartFraction negative b Over 2 a EndFraction, f (StartFraction negative b Over 2 a))

What is the vertex of the function?

(
,
)

Answer 1

vertex = (4, - 25 )

Explanation:

Given a quadratic function in standard form : f(x) = ax² + bx + c : a ≠ 0

The the x- coordinate of the vertex is

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

f(x) = x² - 8x - 9 ← is in standard form

with a = 1, b = - 8, thus

`x_(V)` = -
`(-8)/(2)` = 4

Substitute x = 4 into f(x) for corresponding value of y

f(4) = 4² - 8(4) - 9 = 16 - 32 - 9 = - 25

vertex = (4, - 25 )

Answer 2

vertex is (4,-25)

Explanation:

`f(x) = x^2 - 8x - 9`

To find out the vertex we use formula

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

From the given f(x), the value of a=1, b=-8 and c=-9

Plug in the values in the formula

`x=(-(-8))/(2(1))`

x=4

Now find the value of y

plug in 4 for x in f(x)

`f(4) = 4^2 - 8(4)- 9=-25`

The value of y is -25

The vertex is (4,-25)