Wyznacz wierzchołek paraboli o równaniu

Question

A}f[x]=-3[x+1]²    b}y=x²+4x-13     c}f[x]=-3x²+3

Answer 1

W=[p,q]

a) f(x)=-3(x+1)²= -3(x²+2x+1)= -3x+6x+3
a=-3
b=6
c=3

p=-b/2a
p=-6/2*(-3)=-6/-6=1

q=-Δ/4a
Δ= b² - 4ac=6² - 4*(-3*3)=36-4*(-9)=36+36=72
q=-72/4*(-3)
q=-72/-12
q= 6

W=[1,6]

b)y=x²+4x-13
a=1
b=4
c=-13

p=-b/2a
p=-4/2=-2

q=-Δ/4a
Δ= b² - 4ac= 4² - 4(-13)=16+52= 68

q=-68/4= -17

W=[-2;-17]

c)f(x)=-3x²+3
a=-3
b=0
c=3

p=0
q=f(p)=3

W=[0,3]