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## on Nov 21, 2010

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Find vertex, roots and sketch parabolas

Find vertex, roots and sketch parabolas

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• How To Graph Quadratic Equations
• Getting Started
• The standard form of a quadratic equation is y = ax 2 + bx + c.
• The graph of a quadratic equation is a parabola .
• When a is positive , the graph opens up .
• When a is negative , the graph opens down.
• Every parabola has a vertex . For graphs opening up, the vertex is a minimum (low point). For graphs opening down, the vertex is a maximum (high point).
• The x-coordinate of the vertex is equal to .
• Find the Vertex You are given the equation y=-x 2 + 4x –1 . Find the coordinates of the vertex. The coordinates of the vertex are (2,3) To find the x coordinate of the vertex, use the equation Then substitute the value of x back into the equation of the parabola and solve for y . x b a   2 x  2    a b 1 4 , (  x   4 2 1 )( ) 2 y x x     4 1 y     4 8 1 y  3 y     2 2 4 2 1 ( ) ( )
• Table of Values
• Choose two values of x that are to the right or left of the x- coordinate of the vertex.
• Substitute those values in the equation and solve for y .
• Graph the points.
• Since a parabola is symmetric, you can plot those same y- values on the other side of the parabola, the same distance away from the vertex.
x y = - x 2 + 4 x -1 y 1 -1 y = -(1) 2 + 4(1) - 1 y = -1 +4 - 1 2 y = -(-1) 2 + 4(-1) -1 y = -1 -4 -1 -6
• Graph the Parabola Plot the vertex and the points from your table of values: (2,3), (1,2), (-1,-6). Since a parabola is symmetric and has a vertical line of symmetry through the vertex of the parabola, points which are the same distance to the right of the vertex will also have the same y-coordinate as those to the left of the vertex. Therefore, we can plot points at (3,2) and (5,-6). Sketch in the parabola. x y
• You Try It Find the vertex of the following quadratic equations. Make a table of values and graph the parabola.
• Problem 1 The vertex is at (2,-4) x y
• Problem 2 The vertex is at (0,3) x y
• Problem 3 The vertex is at (3,-5) x y