Learning Resources

Focus C: Forms of Quadratic Functions

Follow the graphing of the function by clicking on the Go forward one frame button below and see the finished graph. Use the other Global Action buttons to navigate through the window.

• The graph has a minimum y-value since there is a lowest point on the graph above.

• The graph opens upward. This can be deduced from the equation since the 2 is positive it must open upward.

• It has the same basic shape as ; however it is stretched vertically by a factor of  ; again this can be found from the equation since the vertical stretch is the reciprocal of the 2.

• The line or axis of symmetry is ; this can be seen on the graph or from the (x - 5) in the equation .

• Unless the graph is extended you will not be able to read the y-intercept from the graph; however, you can calculate it by letting the x = 0 in the equation and solving for y gives the y- intercept as (0, 13.5). 

• From the graph there are no x-intercepts since the total graph is above the x-axis.

• The vertex is (5,1) which you can read from the graph or directly from the equation.