by Elizabeth Estes 12 years ago
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If not, use the quadratic equation to find the zeros
x equals negative B plus or minus square root B squared minus four A*C all over two A. Where A,B and C are defined by the standard form of a quadratic equation as written above.
Be careful not to drop negative signs
Remember that you cannot take the square root of a negative number
If everything under the radical is negative, the graph does not intersect the x-axis. (everything under the radical is called the descriminant because it descriminates between 3 forms of quadratics. Those with two zeros and a positive determinant, those with one zero and a determinant of zero, and those with no zeros and a negative determinant)
When you have finished solving the quadratic formula, x will equal the zeros of the function. In other words, you have now located where the graph of the equation intersects the x-axis.
If there are no zeros (negative descriminant) than skip this step for now and move on to the next step.
Plot the Zeros on the coordinate plane. (aka. graph the points of the x-intercepts)
Find the axis of symmetry by using the equation x=-b/2a and the definition of A, B and C as defined in the beginning.
Use this new x-value to find its cooresponding y-value by plugging the x-value into the original equation and solving for y.
These x and y values are the coordinants of the vertex of the quadratic equation. You can now plot this point on your graph.
You now must use your knowledge of what the parent function of quadratic equations looks like to finish drawing your graph.
If yes, than factor it.
Once it has been factored, set the equation equal to zero by replacing "y" with zero.
Find the "zeros" of the function by splitting it into two equations that are both equal to zero and solving them.
x will now equal the zeros of the function. In other words, you have now located where the graph of the equation intersects the x-axis.
