2. y = -2x² + 8xAxis of Symmetry:Vertex:Domain:Range:​

Answer:Part 1) The axis of symmetry is x=2Part 2) The vertex is the point (2,8)Part 3) The domain is all real numbersPart 4) The range is all real numbers less than or equal to 8Step-by-step explanation:we have[tex]y=-2x^{2}+8x[/tex]This is a vertical parabola open downward (because the leading coefficient is negative)The vertex represent a maximumstep 1Find the vertexConvert the quadratic equation in vertex formFactor -2 leading coefficient[tex]y=-2(x^{2}-4x)[/tex]Complete the square[tex]y=-2(x^{2}-4x+4)+8[/tex]rewrite as perfect squares[tex]y=-2(x-2)^{2}+8[/tex]soThe vertex is the point (2,8)step 2Find the axis of Symmetrywe know thatIn a vertical parabola, the axis of symmetry is equal to the x-coordinate of the vertexthe vertex is the point (2,8)thereforeThe axis of symmetry is x=2step 3Find the domainThe domain of the quadratic equation is the interval ------> (-∞,∞)The domain is all real numbersstep 4Find the rangeThe range of the quadratic equation is the interval ------> (-∞,8][tex]y\leq 8[/tex]The range is all real numbers less than or equal to 8