Question

Encontre as coordenadas do vértice de cada função quadrática:
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Answer 1

Explicação passo-a-passo:

7)

a)

$y = {x}^{2} - 4x + 3 \\ \\\boxed{\bf V \left( - \frac{b}{2a} , \frac{ - \Delta}{4a} \right)} \\ \\ xv = \frac{ - ( - 4)}{2(1)} \\ \\ xv = \frac{4}{2} \\ \\ \Large \boxed{ xv \bf = 2} \\ \\\Large\boxed{\Delta = b^2-4ac}\\ \\ yv = - \frac{(( - 4) {}^{2} - 4(1)( 3)) }{4(1)} \\ \\ yv = - \frac{(4 - 12)}{4} \\ \\ yv = - \frac{( - 8)}{4} \\ \\ yv = \frac{8}{4} \\ \\ \Large \boxed{yv = 2} \\ \\ \Large \boxed{ \green{ V \bf(2,2)}}$

b)

$y = {x}^{2} - 6x + 9 \\ \\ xv = \frac{ - ( - 6)}{2(1)} \\ \\ xv = \frac{6}{2} \\ \\ \Large \boxed{xv = 3} \\ \\ yv = f(3) \\ \\ yv = {3}^{2} - 6(3) + 9 \\ \\ yv = 9 - 18 + 9 \\ \\ yv = - 9 + 9 \\ \\ \Large \boxed{ yv = 0} \\ \\ \Large \boxed{ \green{V\bf(3,0)}}$

c)

$y = {x}^{2} - 9 \\ \\ xv = \frac{ - 0}{2(1)} \\ \\ \Large\boxed{ xv = 0} \\ \\ yv = f(0) \\ \\ yv = {0}^{2} - 9 \\ \\ \Large \boxed{ yv = - 9} \\ \\ \Large \boxed{ \green{ V\bf(0,- 9)}}$

d)

$y = {x}^{2} - 6x + 8 \\ \\ xv = \frac{ - ( - 6)}{2(1)} \\ \\ xv = \frac{6}{2} \\ \\ \Large \boxed{xv = 3} \\ \\ yv = f(3) \\ \\ yv = {3}^{2} - 6(3) + 8 \\ \\ yv = 9 - 18 + 8 \\ \\ yv = - 9 + 8 \\ \\ \Large \boxed{ yv = - 1} \\ \\ \Large \boxed{ \green{V\bf(3,- 1)}}$

e)

$y = {x}^{2} - 4x \\ \\ xv = \frac{ - ( - 4)}{2(1)} \\ \\ xv = \frac{4}{2} \\ \\ \Large \boxed{xv = 2} \\ \\ yv = f(2) \\ \\ yv = {2}^{2} - 4(2) \\ \\ yv = 4 - 8 \\ \\ \Large \boxed{yv = - 4} \\ \\ \Large \boxed{ \green{V \bf(2, - 4)}}$

f)

$y = 2 {x}^{2} + 8x \\ \\ xv = \frac{ - 8}{2(2)} \\ \\ xv = \frac{ - 8}{4} \\ \\ \Large \boxed{ xv = - 2} \\ \\ yv = f( - 2) \\ \\ yv = 2( - 2) {}^{2} + 8( - 2) \\ \\ yv = 2(4) - 16 \\ \\ yv = 8 - 16 \\ \\ \Large \boxed{yv = - 8} \\ \\ \Large \: \boxed{ \green{ V \bf( - 2, - 8)}} \\ \\ \Large \boxed{ \underline{\blue{ \bf \: Bons \: Estudos!} \: \bf 20/05/2021}}$