Reflections over the x axis

[ErinSwallow]

Okay so there’s a quadratic equation graphed and we’re doing reflections. My math teacher said if the lowest y value in the line goes lower than zero, it’s not called a reflection over the x axis. Is that true?

 

[Steven G]

You say ...if the lowest point in line... What line??!!
What is not called a reflection over the x-axis?? You can reflect anything graph across any line including the x-axis.

Please post your question a little better. Thanks!

 

[Otis]

there’s a quadratic equation graphed … My math teacher said if the [smallest] y value [is less] than zero, it’s not called a reflection over the x axis. Is that true?

Hi Erin. The answer is yes, if you're talking about a parabola that opens upward and the bottom part of that parabola lies below the x-axis. In such a graph, nothing has been reflected.

Here's an example of what I'm thinking.

y = 2x^2 - 16x - 16



Part of the parabola lies below the x-axis, two points of the parabola lie directly on the x-axis, and the remaining part of the parabola lies entirely above the x-axis.

If we plot the absolute value of 2x^2-16x-16, instead, then the part below the x-axis above will be reflected across that axis, in the new graph.

y = | 2x^2 - 16x - 16 |



If we multiply the polynomial by -1, then the entire parabola is reflected across the x-axis. Every y-value that was positive in the first graph above becomes negative, and every y-value that was negative becomes positive. This effectively reflects every point (except for the x-intercepts) across the x-axis, flipping the entire parabola.

y = -(2x^2 - 16x - 16)



I hope these images help you understand what reflections are. Please feel free to add any questions you may have.

?

 

[ErinSwallow]

Hi Erin. The answer is yes, if you're talking about a parabola that opens upward and the bottom part of that parabola lies below the x-axis. In such a graph, nothing has been reflected across the x-axis.

Here's an example of what I'm thinking.

y = 2x^2 - 16x - 16

View attachment 23103

Part of the parabola lies below the x-axis, two points of the parabola lie directly on top of the x-axis, and the remaining part of the parabola lies entirely above the x-axis.

If we plot the absolute value of 2x^2-16x-16, instead, then the part below the x-axis (above) will be reflected across the x-axis, in the new graph.

y = | 2x^2 - 16x - 16 |

View attachment 23104

If we multiply the polynomial by -1, then the entire parabola is reflected across the x-axis. (Every y-value that was positive in the first graph above becomes negative, and every y-value that was negative becomes positive. This effectively reflects every point (except for the x-intercepts) across the x-axis, flipping the entire parabola.

y = -(2x^2 - 16x - 16)

View attachment 23105

I hope these images help you understand what reflections are. Please feel free to add any questions you may have.

?

Thank you so much!! yeah I thought so, thanks