Question

Consider the following qaudratic function .f(x)=9x^2

Answer 1

Question:

Consider the following quadratic function. f(x) = −9x^2 + 16x − 13.

Identify the vertex

Answer:

`((8)/(9),-(53)/(9))`

Explanation:

Given

`f(x) = -9x^2 + 16x - 13`

Required

Identify the vertex

The vertex of an equation is represented as:

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

i.e.

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

In
`f(x) = -9x^2 + 16x - 13`

`a= -9`
`b = 16`
`c = -13`

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

`x = -(16)/(2 * -9)`

`x = (16)/(2 * 9)`

`x = (8)/(9)`

Substitute 8/9 for x in
`f(x) = -9x^2 + 16x - 13`

`f(8/9) = -9(8/9)^2 + 16(8/9) - 13`

`f(8/9) = -9(64/81)+ (16*8/9) - 13`

`f(8/9) = -64/9 + (128/9) - 13`

Take LCM

`f((8)/(9)) = (-64 + 128 -117)/(9)`

`f((8)/(9)) = (-53)/(9)`

`f((8)/(9)) = -(53)/(9)`

Hence, the vertex is:

`((8)/(9),-(53)/(9))`