1 / 11

Can we get information about the graph from the equation?

Can we get information about the graph from the equation?. Do Now: Graph the equation y=x 2. What happens if we change the value of a?. When we change the value of a, the shape of the graph will change. If a is positive, then the parabola will open up.

kalonice-cleatus
Download Presentation

Can we get information about the graph from the equation?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Can we get information about the graph from the equation? Do Now: Graph the equation y=x2

  2. What happens if we change the value of a? • When we change the value of a, the shape of the graph will change. • If a is positive, then the parabola will open up. • If a is negative, the parabola will open down. • If a is greater than one, the graph will be narrower. • If a is less than one, the graph will be wider.

  3. Y=x2, y=2x2, y=-x2, y=.5x2

  4. How else can the graph change? • The graph can also shift up and down. • If a constant is added or subtracted to the standard y=x2 equation, then the graph will shift up or down an equal number of units.

  5. y=x2+3, y=x2-3

  6. Can the graph shift side to side? • Yes, this happens when we add or subtract a constant to x BEFORE we square it. • Instead of the standard y=x2 equation, the equation looks like y=(x-2)2 or y=(x+2)2 • If the number is positive, the shift is to the right, if it is negative, the shift is to the left.

  7. y=(x-2)2, y=(x+2)2

  8. How can we get this information if we have an equation in standard form? • You already have the tools needed to pick out these shifts just from the standard form. • Complete the square • Do all the same steps as before, but instead of taking the square root of both sides, solve for x

  9. Example • Compare the graph of y=x2-2x-3 to the standard y=x2 Y=x2-2x-3 Y+3=x2-2x Y+3+1=x2-2x+1 Y+4=(x-1)2 Y=(x-1)2-4 The graph shifts down 4 and to the right 1 Original equation Get x’s alone Add half of b squared Factor Isolate y Explain differences

  10. Terminology • When we have an equation written in the form y=a(x-h)2+k, we know the vertex of the parabola. • The vertex is the maximum or minimum of the graph and is located at (h, k) • Note: The x value of the vertex can be found by finding -b/2a from the standard equation. Then plug this value into the equation to find the y value. • The line x=h is called the axis of symmetry

  11. Summary • How can completing the square give us information about the graph of a quadratic equation? • HW: pg 95, #1, 3

More Related