The graph of a quadratic equation or function can tell us a lot about it. When using a the graph to solve a quadratic equation that is equal to zero (in standard from) then you are trying to idnetify where the graph crosses the x-axis. This is because that is where the input values (x values) produce output values (y values) equal to zero.
Use the sliders to change the values of a, b, and c. Notice how these values affect the graph of the function and where it crosses the x-axis.
Here are some more things to explore regarding the graph:
Can you make it so that the graph never crosses the x-axis? Are there different ways to accomplish this? What does that mean for the solutions?
Can you make so the graph only crosses the x-axis once?
Try un-checking the show root buttons and see how accurately you can approximate the solutions.
Skill Practice:
Graph each of the equations and state the solutions as accurately as you can.
Understanding the Graph
The graph of a quadratic equation or function can tell us a lot about it. When using a the graph to solve a quadratic equation that is equal to zero (in standard from) then you are trying to idnetify where the graph crosses the x-axis. This is because that is where the input values (x values) produce output values (y values) equal to zero.
Use the sliders to change the values of a, b, and c. Notice how these values affect the graph of the function and where it crosses the x-axis.
Here are some more things to explore regarding the graph:
Can you make it so that the graph never crosses the x-axis? Are there different ways to accomplish this? What does that mean for the solutions?
Can you make so the graph only crosses the x-axis once?
Try un-checking the show root buttons and see how accurately you can approximate the solutions.
Skill Practice:
Graph each of the equations and state the solutions as accurately as you can.If you need help or review graphing quadratics here is thorough explanation from the University of Georgia: Web Link