Y=3x²-6x+2 answer this with solution picture
Answer (1)
Answer:The given quadratic function is Y = 3x² - 6x + 2. To analyze or solve this, we can find its vertex, roots, or other properties.First, let's find the vertex of the parabola. The x-coordinate of the vertex for a quadratic in the form y = ax² + bx + c is given by -b/(2a). Here, a = 3 and b = -6.Calculating the x-coordinate:x = -(-6) / (2 * 3) = 6 / 6 = 1.Next, substitute x = 1 back into the original equation to find the y-coordinate:Y = 3(1)² - 6(1) + 2 = 3 - 6 + 2 = -1.Thus, the vertex of the parabola is at (1, -1).To find the roots (x-intercepts), set Y to zero and solve for x:0 = 3x² - 6x + 2.Divide through by 3 to simplify:0 = x² - 2x + /3.Using the quadratic formula x = [-b ± sqrt(b² - 4ac)] / (2a), where a=1, b=-2, c=2/3:Discriminant D = (-2)² - 4*1*(2/3) = 4 - (8/3) = (12/3) - (8/3) = 4/3.Since D > 0, there are two real roots:x = [2 ± sqrt(4/3)] / 2.Simplify sqrt(4/3):sqrt(4/3) = (2 / sqrt(3))Therefore,x = [2 ± (2 / sqrt(3))] / 2.Divide numerator and denominator by 2:x = [1 ± (1 / sqrt(3))].Rationalizing the denominator:x = [1 ± (sqrt(3)/3)].Hence, the roots are approximately:- x ≈ 1 + (sqrt(3)/3)- x ≈ 1 - (sqrt(3)/3)This completes the analysis of the quadratic function Y=3x² -6x +2.Step-by-step explanation:
