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:

$(\frac{8}{9},-\frac{53}{9})$

Step-by-step explanation:

Given

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

Required

Identify the vertex

The vertex of an equation is represented as:

$(x,f(x)) = (\frac{-b}{2a},f(x))$

i.e.

$x = -\frac{b}{2a}$

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

$a= -9$    $b = 16$   $c = -13$

$x = -\frac{b}{2a}$ becomes

$x = -\frac{16}{2 * -9}$

$x = \frac{16}{2 * 9}$

$x = \frac{8}{9}$

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

$f(\frac{8}{9}) = \frac{-64 + 128 -117}{9}$

$f(\frac{8}{9}) = \frac{-53}{9}$

$f(\frac{8}{9}) = -\frac{53}{9}$

Hence, the vertex is:

$(\frac{8}{9},-\frac{53}{9})$