Please help me solve rewrite the function in vertex form and state the vertex (h,k)
Answer (1)
Answer:9.) To solve the quadratic equation y = 2x² - 8x + 5, we can try to factor it or use the quadratic formula. Let's use the quadratic formula since factoring doesn't seem straightforward:## Quadratic FormulaThe quadratic formula is given by:$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$For the equation y = 2x² - 8x + 5, we have:- a = 2- b = -8- c = 5## Plugging in the ValuesLet's plug these values into the quadratic formula:$$x = \frac{-(-8) \pm \sqrt{(-8)^2 - 4(2)(5)}}{2(2)}$$$$x = \frac{8 \pm \sqrt{64 - 40}}{4}$$$$x = \frac{8 \pm \sqrt{24}}{4}$$$$x = \frac{8 \pm 2\sqrt{6}}{4}$$$$x = 2 \pm \frac{\sqrt{6}}{2}$$## SolutionsSo, the solutions to the equation are:$$x = 2 + \frac{\sqrt{6}}{2}$$$$x = 2 - \frac{\sqrt{6}}{2}$$These are the values of x that make y = 0.If you'd like to find the vertex of the parabola or graph the equation, just let me know!10.) To solve the quadratic equation y = 2x² + 4x + 4, we can try to factor it or use the quadratic formula. Let's use the quadratic formula:## Quadratic FormulaThe quadratic formula is given by:$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$For the equation y = 2x² + 4x + 4, we have:- a = 2- b = 4- c = 4## Plugging in the ValuesLet's plug these values into the quadratic formula:$$x = \frac{-4 \pm \sqrt{4^2 - 4(2)(4)}}{2(2)}$$$$x = \frac{-4 \pm \sqrt{16 - 32}}{4}$$$$x = \frac{-4 \pm \sqrt{-16}}{4}$$$$x = \frac{-4 \pm 4i}{4}$$$$x = -1 \pm i$$## SolutionsSo, the solutions to the equation are complex numbers:$$x = -1 + i$$$$x = -1 - i$$These complex solutions indicate that the quadratic equation y = 2x² + 4x + 4 does not intersect the x-axis and therefore has no real roots.If you'd like to explore further or have any specific questions about complex numbers, feel free to ask!
