Graphs of quadratic equations are always known as parabolas. Parabolas are "U" shaped curves.
The Y-Intercept of a quadratic equation always comes from the "C" part of any equation that we discovered in "The Formula" area of this site.
For example, the equation 4x2 + 2x - 5 = 0 has C at -5.
Therefore the graph of the equation 4x2 + 2x -5 = 0 is shown below,
To calculate were the graph intercepts the X axis you must first work out the solutions to the equation. You can do this by visiting the home area of the website.
For example, the roots of 1x2 + 1x - 2 = 0 are, 1 and -2. This tells us that the graph cuts the x axis at 1 and -2. We also know that the graph intercepts the Y axis at -2. So the graoh looks like,
If an equation has no real roots, this means that the graph does not cross the x axis, for example, the equation,
1x2 + 10 + 34 = 0 has no real roots. The graph does however cross the y axis at 34. So it could look like,
A quadratic eqation can also have equal roots.
A quadratic equation can also have equal roots. This is where both the solutions to the quadratic are the same. For instance,
1x2 - 8x + 16 = 0
The solutions to the above are 4 and 4. When this happens, it means that the graph of the equation touches the x axis at that point.
So, 1x2 - 8x + 16 = 0 looks like,
Finally, when the "a" term of a quadratic is negative, the entire graph gets flipped upside down. For instance the solutions of,
-x2 + 4x - 4 = 0
are, 2 and 2. So the graph must touch the x axis at 2 and cross the y axis at -4. Also, the "a" term is negative so the graph must be upside down,
Here is what it looks like,
