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Published byReynold Walters Modified over 5 years ago

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Graphs of Quadratic Equations

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Standard Form: y = ax 2 +bx+ c Shape: Parabola Vertex: high or low point

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Axis of Symmetry: Line that divides parabola into two parts that are mirror image of each other. Axis of Symmetry Vertex

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The vertex has an x-coordinate of The axis of symmetry is the vertical line passing through

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y = x 2 First find the vertex. This is the x value of the vertex, now find the y value. If x = 0, y = 0 Vertex = (0,0) 0 is the axis of symmetry:

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Example: y = x 2 Make a table for y = x 2 Since the vertex is (0,0), pick an x value to the right and left of 0.

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To graph a Quadratic Equation y = ax 2 +bx+cy = -ax 2 +bx+c If a is positive, the parabola opens up If a is negative, the parabola opens down

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Graph Points Line of symmetry A is positive 1, so the parabola opens up with (0,0) as the low point.

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GRAPH: y = x 2 -x-6 Identify the a, b, and c values First find the vertex Make a table with an x value to the right and left of the vertex x value Graph these points and connect. Label the vertex

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Find vertex and plug in to find y. value to have high or low point. 1.

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The x value of the vertex is 1 / 2 Now find the y value of the vertex by plugging x back into the equation. y = x 2 -x-6 y = ( 1 / 2 ) 2 – ½ - 6 The y value is - 25 / 4. Now pick a point to the left and right of ½.

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GRAPH : y = x 2 -x-6 I try to pick points equal distance from the vertex x value. I also tried 0 here.

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Vertex low Y=x 2 -x-6 opens up (a positive) line of symmetry x =

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Line of Symmetry Graph: y= -2x 2 +2x+1 a is negative- opens down = 1 2 Find the y value, then pick a point to the left and right of 1/2 to see how to draw the parabola.

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- 2 - - 2 2 2 -

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y=-2x 2 +2x+1

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Use parabola to find the height of a shot put. Height in feet Distance in feet 34.15 Vertex is height

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Equation: y= -.01464x 2 +x+5 USE CALCULATOR!

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Put x back in to find y value y = -.01464(34.15) 2 +34.15+5 = 22.08 ft. high (34.15,22.08) vertex (high point)

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