Question

A funçao y= x² - px + q tem seu vertice no ponto (3,-4) . Calcule P e Q

Answer 1

$X_{v}=3\\Y_{v}=-4$
____________________________

Fórmula do x do vértice: Xv = -b/2a

$X_{v}=-\dfrac{b}{2a}\\\\\\3=-\dfrac{(-p)}{2\cdot1}\\\\\\3=\dfrac{p}{2}\\\\\\3*2=p\\\\\boxed{\boxed{p=6}}$

Podemos achar o y do vértice substituíndo x por Xv (x do vértice) na função:

$y=x^{2}-px+q\\y=x^{2}-6x+q\\Y_{v}=(X_{v})^{2}-6(X_{v})+q\\-4=3^{2}-6(3)+q\\-4=9-18+q\\-4=-9+q\\-4+9=q\\\\\\\boxed{\boxed{q=5}}$