Question

PLSSSSSSSSSSS HELPPP>> Show work solve the sysytem- y=1/2x^2+4x+4 y=-4x+12 1/2

Answer 1

(1, 8.5 ) and ( - 17, 80.5 )

Explanation:

Given the 2 equations

y =
`(1)/(2)` x² + 4x + 4 → (1)

y = - 4x + 12
`(1)/(2)` → (2)

Substitute (1) into (2), that is

`(1)/(2)` x² + 4x + 4 = - 4x + 12
`(1)/(2)` ( 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 )