Question

Someone please help. thanks!

Answer 1

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: $\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\dfrac{-(10)\pm \sqrt{(10)^2-4(3)(5)}}{2(3)}\\\\\\.\ =\dfrac{-10\pm \sqrt{100-60}}{6}\\\\\\.\ =\dfrac{-10\pm \sqrt{40}}{6}\\\\\\.\ =\dfrac{-10\pm 2\sqrt{10}}{6}\\\\\\.\ =\dfrac{-5\pm \sqrt{10}}{3}$

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