Question

Determine o vértice da parábola f(x) = x2 -5x + 4.

Answer 1

$f(x)=x^2-5x+4$

$a=1~~~~~b=-5~~~~~c=4$

$x_{\text{V}}=\dfrac{-b}{2\cdot a}$

$x_{\text{V}}=\dfrac{-(-5)}{2\cdot1}~\hookrightarrow~\boxed{x_{\text{V}}=\dfrac{5}{2}}$

$y_{\text{V}}=\dfrac{-\Delta}{4\cdot a}$

$\Delta=b^2-4\cdot a\cdot c$
$\Delta=(-5)^2-4\cdot1\cdot4$
$\Delta=25-16$
$\Delta=9$

$y_{\text{V}}=\dfrac{-9}{4\cdot1}~\hookrightarrow~\boxed{y_{\text{V}}=-\dfrac{9}{4}}$

$\text{V}\left(\dfrac{5}{2},-\dfrac{9}{4}\right)$