Funkcja kwadratowa f dana jest wzorem : f(x)=x²+6x+8 .
f(x) > 0
x²+6x+8 > 0
Δ=6²-4·1·8=36-32=4 , √Δ=√4=2
x1=(-6-2)/2
x1=-4
x2=(-6+2)/2
x2=-2
x∈(-∞,-4)∪(-2,∞)
[tex]f(x) = x^{2}+6x+8\\\\x^{2}+6x+8 > 0\\\\a = 1, \ b = 6, \ c = 8\\\\\Delta = b^{2}-4ac = 6^{2}-4\cdot1\cdot8 = 36 - 32 = 4\\\\\sqrt{\Delta} = \sqrt{4} = 2\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-6-2}{2\cdot1} = \frac{-8}{2} = -4\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{-6+2}{2} = \frac{-4}{2} = -2[/tex]
a > 1, ramiona paraboli zwrócone do góry
x ∈ (-∞; -4) ∪ (-2; +∞)
