Question

sa se determine m apartine R, stiind ca varful parabolei asociate funcţiei f(x)= x^2 - mx + 2 are coordonate egale

Answer 1

m ∈ IR ?
f(x) = x² - mx + 2 
V(x;y) 
$x_v = y_v \\ - \frac{b}{2a} = - \frac{delta}{4a} \\ \frac{-m}{2} = \frac{m^2-8}{4} \\ -2m = m^2 - 8 \\ m^2+2m-8 = 0$
Δ = 4 + 32 = 36
$m_1 = \frac{-2+6}{2} = \frac{4}{2} = 2$
$m_1 = \frac{-2-6}{2} = \frac{-8}{2} = -4$
m ∈ {-4;2}