Determine the equation for the parabola graphed below?

Answer:y = [tex]\frac{1}{2}[/tex] x² - 2x + 1Step-by-step explanation:The equation of a parabola in vertex form isy = a(x - h)² + kwhere (h, k) are the coordinates of the vertex and a is a multiplierFrom the graph (h, k) = (2, - 1), thusy = a(x - 2)² - 1 To find a substitute a point on the curve (0, 1) into the equation1 = 4a - 1 ( add 1 to both sides )4a = 2 ( divide both sides by 4 )a = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex], hencey = [tex]\frac{1}{2}[/tex](x - 2)² - 1 ← in vertex formExpand the factor and simplifyy = [tex]\frac{1}{2}[/tex](x² - 4x + 4) - 1   = [tex]\frac{1}{2}[/tex] x² - 2x + 2 - 1   = [tex]\frac{1}{2}[/tex] x² - 2x + 1 ← in standard form