Respuesta :
Answer:
(1, 8.5 ) and ( - 17, 80.5 )
Step-by-step explanation:
Given the 2 equations
y = [tex]\frac{1}{2}[/tex] x² + 4x + 4 → (1)
y = - 4x + 12 [tex]\frac{1}{2}[/tex] → (2)
Substitute (1) into (2), that is
[tex]\frac{1}{2}[/tex] x² + 4x + 4 = - 4x + 12 [tex]\frac{1}{2}[/tex] ( multiply through by 2 to clear the fractions )
x² + 8x + 8 = - 8x + 25 ( add 8x to both sides )
x² + 16x + 8 = 25 ( subtract 25 from both sides )
x² + 16x - 17 = 0 ← in standard form
(x + 17)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 17 = 0 ⇒ x = - 17
x - 1 = 0 ⇒ x = 1
Substitute these values into either of the 2 equations and evaluate for y
Substituting into (2 )
x = 1 : y = - 4(1) + 12.5 = - 4 + 12.5 = 8.5 ⇒ (1, 8.5 )
x = - 17 : y = - 4(- 17) + 12.5 = 68 + 12.5 = 80.5 ⇒ (- 17, 80.5 )
