Question

determine o vértice da parábola

Y= x² -5x +6

2) y= -x² +8x -15

3) y= 3x -4x²

por favor alguém me ajuda

Answer 1

$y = - \frac{Delta}{4a}$

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


a) $y = x^{2} -5x + 6$
a = 1
b = -5
c = 6

Delta = b² - 4·a·c
Delta = (-5)² - 4·1·6
Delta = 25 - 24
Delta = 1

$x = - \frac{b}{2a}$
$x = - \frac{(-5)}{2*1}$
$x = \frac{5}{2}$

$y = - \frac{Delta}{4*a}$
$y = - \frac{1}{4*1}$
$y = - \frac{1}{4}$

∴ Vértice = $( \frac{5}{2} , -\frac{1}{4} )$


b) $y = - x^{2} +8x -15$
a = -1
b = 8
c = -15

Delta = b² - 4·a·c
Delta = 8² - 4·(-1)·(-15)
Delta = 64 - 60
Delta = 4

$x = - \frac{b}{2*a}$
$x = - \frac{8}{2*(-1) }$
$x = \frac{8}{2}$
$x = 4$

$y = - \frac{Delta}{4*a}$
$y = - \frac{4}{4*(-1)}$
$y = 1$

∴ Vértice = $( 4,1)$


c) $y = 3x-4 x^{2}$
a = -4
b = 3
c = 0

Delta = b² - 4·a·c
Delta = 3² - 4·(-4)·0
Delta = 9

$x = - \frac{b}{2*a}$
$x = - \frac{3}{2*(-4) }$
$x = \frac{3}{8}$

$y = - \frac{Delta}{4*a}$
$y = - \frac{9}{4*(-4)}$
$y = \frac{9}{16}$

∴ Vértice = $( \frac{3}{8} , \frac{9}{16} )$


Att,

Anderson