Answer: (-0.61, 5.85) and (-2.72, 3.04)
Step-by-step 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: [tex]\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{-(10)\pm \sqrt{(10)^2-4(3)(5)}}{2(3)}\\\\\\.\ =\dfrac{-10\pm \sqrt{100-60}}{6}\\\\\\.\ =\dfrac{-10\pm \sqrt{40}}{6}\\\\\\.\ =\dfrac{-10\pm 2\sqrt{10}}{6}\\\\\\.\ =\dfrac{-5\pm \sqrt{10}}{3}[/tex]
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
