Question

Someone please help. thanks!

Answer 1

Answer: (-0.61, 5.85) and (-2.72, 3.04)

Explanation:

y = 2x² + 8x + 10

y = -x² - 2x + 5

Use substitution method to get: 2x² + 8x + 10 = -x² - 2x + 5

Move everything to one side and 0 on the other: 3x² + 10x + 5 = 0

Use the quadratic formula to solve for x:
`(-b\pm √(b^2-4ac))/(2a)`

`x=(-(10)\pm √((10)^2-4(3)(5)))/(2(3))\\\\\\.\ =(-10\pm √(100-60))/(6)\\\\\\.\ =(-10\pm √(40))/(6)\\\\\\.\ =(-10\pm 2√(10))/(6)\\\\\\.\ =(-5\pm √(10))/(3)`

x₁ = -0.61 x₂ = -2.72

Next, input the x-values to solve for y:

y₁ = -x² - 2x + 5 y₂ = -x² - 2x + 5

= -(-0.61)² - 2(-0.61) + 5 = -(-2.72)² - 2(-2.72) + 5

= -0.37 + 1.22 + 5 = -7.40 + 5.44 + 5

= 5.85 = 3.04