A More In Depth Look at the Parabola
ax2 + bx + c = y
All of these equations pass through the point y = 1. We can conclude that the constant c will effect where the parabola crosses the y axis.
In the assignment “Parabola: Friend of Foe” we can see graphs when b and c are constant. b = 1 and c = 0. Below is an example of some graphs with a changing.
The equation of the parabolas to the left are in the form of x2 + x + c = y, where c is a constant. The values for c in the graph are -3, -2, -1, 0, 1, and 2, and 3. From the graph and the equation we can conclude that the constant c changes where the parabola crosses the y axis.
Now that we know how the constants effect the parabola, let us look at the first graph again.
By looking at the graph above we can see that x2 +2x + 1 = y and x2 – 2x + 1 = y. Both of these graphs cross the x axis at -1 and 1. We can also see the all of the above graphs cross the y axis at 1. By using this information we can find the roots of an inverted parabola that crosses through all the vertices of the above equations.
The black, inverted parabola’s equation is:
x2 – 1 = y
As we can see, this inverted
parabola has roots at -1 and 1, and has a vertex on the y axis at 1.