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Graphs of Quadratic Functions Day 2

Graphs of Quadratic Functions Day 2. The axis of symmetry is the vertical line passing through the vertex. 1. Find the equation for the axis of symmetry just from symmetric points:. (3, 10) and (15, 10)

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Graphs of Quadratic Functions Day 2

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  1. Graphs of Quadratic Functions Day 2

  2. The axis of symmetry is the vertical line passing through the vertex 1. Find the equation for the axis of symmetry just from symmetric points: • (3, 10) and (15, 10) • Since these ordered pairs are points of symmetry (same y-value, height on graph), you can find the axis of symmetry by finding the middle. • The middle of 3 and 15 is 9. • The axis of symmetry would be x = 9. 2. Find the equation for the axis of symmetry from formula: y = ax2+bx+c

  3. Graph y = - x2 - x + 4 1. Find the axis of symmetry. y = ax2+bx+c a=- , b=-1, and c=4 x = = = = -1 x = -1 is the axis of symmetry 2. Find the vertex. plug in x = -1 y = - (-1)2 – (-1) + 4 y=4.5 Vertex = (-1,4.5)

  4. Graph y = - x2 - x + 4 continued 3. Graph 2 more points Try the y-intercept (c value) y = ax2+bx+c a=- , b=-1, and c=4 y-intercept (0,4) Find more points Select any x value you want and plug into function to find y value (make easy choices, ie. whole numbers Select x=1, and plug in y = - (1)2– (1) + 4 y = - - 1 + 4 y=2.5 makes point (1,2.5)

  5. Graph y = - x2 - x + 4 continued 4. Graph all points and mirror images to make symmetric parabola axis of symmetry x=-1 Vertex (-1,4.5) (0,4) and mirror image (-2,4) (1,2.5) and mirror image (-3,2.5) Check: Opens down because a is negative

  6. Graph Quadratic Example Notes:

  7. Graph y = x2-x-6 1. Find the axis of symmetry. y = ax2+bx+c a=1, b=-1, and c=-6 x = = = x = is the axis of symmetry 2. Find the vertex. plug in x = y = ()2 – () - 6 y = -6 Vertex = (,-6)

  8. Graph y = x2-x-6 continued 3. Graph at least 2 more points Try the y-intercept (c value) y = ax2+bx+c a=1, b=-1, and c=-6 y-intercept (0,-6) Find more points Select any x value you want and plug into function to find y value (make easy choices, ie. whole numbers Select x=3, and plug in Select x=2, and plug in y = ()2 – () - 6 y=0 makes point (3,0) y = ()2 – () - 6 y=-4 makes point (2,-4)

  9. Graph y = x2-x-6 continued 4. Graph all points and mirror images to make symmetric parabola axis of symmetry x = Vertex (,-6) (0,-6) and mirror image (1,-6) (2,-4) and mirror image (-1,-4) (3,0) and mirror image (-2,0) Check: Opens up because a is positive

  10. Additional Practice Problems if needed

  11. Graph:y= -2x2+2x+1 a is negative: opens down Find Line of Symmetry = 1 2 Find the y value, then pick more points to see how to draw the parabola.

  12. 2 - - 2 - 2 2 -

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

  14. Graph:y= x2+5x-14 Will open up b/c a is positive Find axis of symmetry and the vertex Plug back in for y and solve

  15. Change to common denominators Vertex is

  16. Vertex is Can also find x intercepts of y = x2 + 5x - 14 by factoring to find solutions (2,0) and (-7,0) y -7 x 2

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