Graphing Quadratic Equations Using the Axis of Symmetry
A quadratic equationis apolynomialequation of学位 . The standard form of a quadratic equation is
whereandare all real numbers and.
If we replacewith, then we get aquadratic function
whose graph will be aparabola.
The axis of symmetry of this parabola will be the line. The axis of symmetry passes through the vertex, and therefore the-coordinate of the vertex is. Substitutein the equation to find the-coordinate of the vertex. Substitute few more-values in the equation to get the corresponding-values and plot the points. Join them and extend the parabola.
Example 1:
Graph the parabola.
Compare the equation withto find the values of,, and.
Here,and.
Use the values of the coefficients to write the equation of轴线对称metry.
The graph of a quadratic equation in the formhas as its axis of symmetry the line. So, the equation of the axis of symmetry of the given parabola isor.
Substitutein the equation to find the-coordinate of the vertex.
因此,coordinates of the vertex are.
Now, substitute a few more-values in the equation to get the corresponding-values.
Plot the points and join them to get the parabola.
Example 2:
Graph the parabola.
Compare the equation withto find the values of,, and.
Here,and.
Use the values of the coefficients to write the equation of axis of symmetry.
The graph of a quadratic equation in the formhas as its axis of symmetry the line. So, the equation of the axis of symmetry of the given parabola isor.
Substitutein the equation to find the-coordinate of the vertex.
因此,coordinates of the vertex are.
Now, substitute a few more-values in the equation to get the corresponding-values.
Plot the points and join them to get the parabola.
Example 3:
Graph the parabola.
Here,is a function of. The parabola opens "sideways" and the axis of symmetry of the parabola is horizontal. The standard form of equation of a horizontal parabola iswhere,, andare all real numbers andand the equation of the axis of symmetry is.
Compare the equation withto find the values of,, and.
Here,and.
Use the values of the coefficients to write the equation of axis of symmetry.
The graph of a quadratic equation in the formhas as its axis of symmetry the line. So, the equation of the axis of symmetry of the given parabola isor.
Substitutein the equation to find the-coordinate of the vertex.
因此,coordinates of the vertex are.
Now, substitute a few more-values in the equation to get the corresponding-values.
Plot the points and join them to get the parabola.