Question

#2 Using transformation, give the equation of each graph. Write the answer of the form y = a(x - h)? + k or x = a(y - k)2 +h a) b) c) 3 3 2 3 4 5 -6-5-4-3-2-1 -2 1 -5 -4 41 -6 - -2 -1 -3 10 12

Answer 1

a x² = 4ay Page No) (a) Given graph is parabola with axis vertical and verlex (-2,-1). We start with the equation of parabola as: o Translate the curve ④ down by unit " New equation becomes = 40 (4+1) Again Translate the curve to the left by a units New equation is (x+2)² = ualy+1) Vertex of this parabola is (-2,-1) the given graph Also from the graph (-1,0) lies in ③ 2. 1=ua .. b. Given graph is (x+2)² = 4+1 (x+23 -1 Given graph is a parabola with axis horizontal and vertex (1,1) We start with equation of Parabola as: y=4ax -O Translate to the right by iunits Equation is Transformed to y² = 40 (x-1)

Page No2 3 Translate ② upward by lunits i. Equation ③ i Transformed to a (y-1)= 40(x-1) Vertex of ③ is (1, 1) and its axis is parallel to xaxis. From the graph (2,0) lies 1=ua x= y-axis. Equation of given graph is (4-1) = x-1 (4-1)+1 (C) Given graph is a parabola with vertex (6,-4) and axis We start with the parabola y=4ax² Translate down wood by u-units 0 ii Transformed to y + 4 4 an² Verlex of this parabola is (o,-4). Given parabola passes through point (1,-5) i From @ - 5+ 4 4a (1) - 4a=-1 Y+4 =-x² ly = -x² - 4 :. Equation of given graph is y = - x² - 4