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Graphs of Quadratic Equations

9.3. Graphs of Quadratic Equations. Standard Form: y = ax 2 +bx+ c. Shape: Parabola. Vertex: high or low point. Axis of Symmetry:. Line that divides parabola into two parts that are mirror image of each other. Axis of Symmetry. Vertex. The vertex has an x-coordinate of.

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Graphs of Quadratic Equations

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  1. 9.3 Graphs of Quadratic Equations

  2. Standard Form: y = ax2+bx+ c Shape: Parabola Vertex: high or low point

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

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

  5. y = x2 First find the vertex. 0 is the axis of symmetry: This is the x value of the vertex, now find the y value. If x = 0, y = 0 Vertex = (0,0)

  6. Example: y = x2 Make a table fory = x2 Since the vertex is (0,0), pick an x value to the right and left of 0.

  7. To graph a Quadratic Equation y = ax2+bx+c y = -ax2+bx+c If a is positive, the parabola opens up If a is negative, the parabola opens down

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

  9. GRAPH: y = x2-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

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

  11. 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 = x2-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.

  12. y = x2-x-6 GRAPH: I try to pick points equal distance from the vertex x value. I also tried 0 here.

  13. Y=x2-x-6 Vertex low opens up (a positive) line of symmetry x =

  14. Graph:y= -2x2+2x+1 a is negative-opens down Line of Symmetry Find the y value, then pick a point to the left and right of 1/2 to see how to draw the parabola. = 1 2

  15. 2 - - 2 - 2 2 -

  16. y=-2x2+2x+1

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

  18. Equation: y= -.01464x2+x+5 USE CALCULATOR!

  19. 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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