Question

Podaj współrzędne wierzchołka paraboli, która jest wykres funkcji:

a) y=2x² - 8x -3

b)y=1/4x²- 5x +3

c)y=-3/8x² +3x +2

Answer 1

A) y=2x² - 8x -3
Δ = 64 - 4*2*(-3) = 88

x = 8/2*2 = 8/4 = 2
y = -88/4*2 = -88/8 = -11

W=(2, -11)

b)y=1/4x²- 5x +3
Δ = 25 - 4 * (1/4) * 3 = 22

x = 5/2*(1/4) = 5/(1/2) = 10
y = -22/4*(1/4) = -22/1 = -22

W = (10, -22)

c)y=-3/8x² +3x +2
Δ = 9 - 4 * (-3/8) * 2 = 12

x = -3/2*(-2/8) = -3/(-4/8) = 6
y = -12/4*(-3/8) = -12/(-12/8) = 8

W = (6, 8)

Answer 2

P=-b/2a q=-Δ/4a (p;q)

a) p=8/4=2 q=-40/8=-5 (2;-5)

Δ=b²-4ac
Δ=64-24
Δ=40

b)y=1/4x²- 5x +3
p= 5/½=10 q=-22/1 (10;-22)
Δ=25-3
=22

c)y=-3/8x² +3x +2

p=4 q=-4 (4;-4)
Δ=9-3=6

Answer 3

A)
y=2x² - 8x -3
Δ = 64 + 24 = 88
W [ -b/2a , -Δ/4a]
W [ 2 , -11]
b)
y=1/4x²- 5x +3
0,25x² - 5x + 3
Δ = 25 - 3 = 22
W [ -b/2a , -Δ/4a]
W [ 10 , - 22]
c)
y=-3/8x² +3x +2
Δ = 9 + 3 = 12
W [ 8 , - 32 ]