Question

In what ways does adding a constant or coefficient to a quadrationc affect the graph

Answer 1

Hope this helps 1)   Equations with negative values for a produce graphs that open down and equations with a positive values for a produce graphs that open up.

2)   As the absolute value of a gets larger our graphs become more narrow (they shoot towards positive or negative infinity faster). This is more interesting than it might appear. If you consider the second derivative of any quadratic it will be the a value. The second derivative represents acceleration, so the larger the a value the faster the increase of velocity and accordingly a quicker progression towards positive or negative infinity. Check this out in graphing calculator, press play to vary the value of a from -20 to 20. Notice that when the value of a approaches zero, the approximates a line, and of course when a is 0 we have the line y = 2x – 1.