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This tutorial will guide you throughthe process of understanding whatthe "Axis of Symmetry" is for a parabolaand how to write an equation for it in theform of "x=h". The axis of symmetry is a vertical line that splitsa parabola into two equal halves. It is a line thata parabola can be reflected over creating itsmirror image. Axis of Symmetry Vertex (0,0) Example: Axis of symmetry Vertex (2,4) To write the equation for the "axis of symmetry",one needs only to indentify the "x" componentof the vertex. This defines the equation for the"axis of symmetry." This "x" value for the vertexis the "h" value in x = h. You can identify the "x" component either visually or by using the following formula: x = -b 2a By looking at theparabola and seeingthat the vertex is locatedat (2, -4), one can writethe equation for the axisof symmetry by noting thatthe x component is 2.Therefore h = 2 and theequation is "x=2". axis of symmetry vertex (2, -4) The x component of the vertex is 2, therefore the equation for the axis of symmetry is: Example: x = 2 vertex (2, 1) axis of symmetry Practice: The x component of the vertex is: ( Vertex is The equation for the axis of symmetry is: x= , ) ( Practice: axis of symmetry x = vertex , ) Practice: What is the equation for the axis of symmetry? x = However, sometimes one can not determine the axis of symmetry by looking at a graph and identifying the "x" component of the vertex. In these situations, one can use the axis of symmetry formula if the equation to the parabola is given. Where "a" and "b" are taken from a quatdraticwritten in standard form; y = ax2 + bx + c x = -b 2a By just looking atthis parabola, it couldbe difficult to determinethe exact point of the vertex. Thereforeit is more difficult towrite the formula to the"axis of symmetry". axis of symmetry x = ? vertex ( ?, ? ) So, one could use the axis of symmetry formula to calculate calculate "h" (the "x" component of the vertex. x = substitute x = -(-6) 2(2) -b 2a = 6 4 = 3 2 y = 2x2 - 6x - 1 Where Equation to the parabola b = -6 a = 2 c = -1 Substititute a and b into the formula The equation to this parabola is: y = -3x2 + 12x - 7 x = x = 2 a = -3 b = 12 c = -7 -(12) 2(-3) = 12 6 x = axis of symmetry x = 2 -b 2a Practice: Determine the axis of symmetry The equation to thisparabola is: x = x = y = x2 - 8x + 10 -b 2a = 2( - ) b = a = c = Calculate the axis of symmetry for the following: y = -3x2 + 6x - 1 x = x = x = -b - 2a 2( ) Caclulate the axis of symmetry for the following: y = 3x2 + 18x - 4 x = x = 2( - ) Calculate the axis of symmetry for the following: y = -5x2 + 30x - 12 x = |