# Thread: need help with quadratic function

1. ## need help with quadratic function

Identify vertex and x intercepts of quadratic function:
$f(x) = x^2 - 8x + 16$

Book's answer:
$f(x) = (x - 4)^2$

x intercept $(4,0)$
vertex $(4,0)$

The answer I came up with using $f(x) = a(x - h)^2 + k$ :
$f(x) = 1(x^2 - 8x + 16) - (1)16 + 16$
$f(x) = x^2 -8x + 16$

I tried strait factoring as well to find the x intercept but got nowhere.
Any suggestions?

2. Originally Posted by dcd5105
Identify vertex and x intercepts of quadratic function:
$f(x) = x^2 - 8x + 16$

Book's answer:
$f(x) = (x - 4)^2$

x intercept $(4,0)$
vertex $(4,0)$

The answer I came up with using $f(x) = a(x - h)^2 + k$ :
$f(x) = 1(x^2 - 8x + 16) - (1)16 + 16$
$f(x) = x^2 -8x + 16$

I tried strait factoring as well to find the x intercept but got nowhere.
Any suggestions?
f(x) is a perfect square, that is: $x^2 - 8x + 16 = (x-4)^2$

In the form $f(x) = a(x-h)^2 + k = 1(x-4)^2 + 0$

The x intercept is where f(x) = 0 and so x=4

The vertex is at (4,0) as this opens downwards and h = 4

3. Originally Posted by dcd5105
Identify vertex and x intercepts of quadratic function:
$f(x) = x^2 - 8x + 16$

Book's answer:
$f(x) = (x - 4)^2$

x intercept $(4,0)$
vertex $(4,0)$

The answer I came up with using $f(x) = a(x - h)^2 + k$ :
$f(x) = 1(x^2 - 8x + 16) - (1)16 + 16$
$f(x) = x^2 -8x + 16$

I tried strait factoring as well to find the x intercept but got nowhere.
Any suggestions?

straight factoring will give you $f(x) = (x - 4)^2$ which is exactly what the book did