All Algebra II Resources
Example Questions
Example Question #21 : Graphing Polynomial Functions
How many -intercepts does the graph of the following function have?
One
Ten
Zero
Two
Five
One
The graph of a quadratic function has an -intercept at any point at which , so, first, set the quadratic expression equal to 0:
The number of -intercepts of the graph is equal to the number of real zeroes of the above equation, which can be determined by evaluating the discriminant of the equation, . Set , and evaluate:
The discriminant is equal to zero, so the quadratic equation has one real zero, and the graph of has exactly one -intercept.
Example Question #22 : Graphing Polynomial Functions
The vertex of the graph of the function
appears in __________.
Quadrant I
None of these
Quadrant IV
Quadrant III
Quadrant II
Quadrant I
The graph of the quadratic function is a parabola with its vertex at the point with coordinates
.
Set ; the -coordinate is
.
Evaluate by substitution:
The vertex has a positive -coordinate and a positive -coordinate, putting it in the upper right quadrant, or Quadrant I.
Example Question #23 : Graphing Polynomial Functions
The vertex of the graph of the function
appears in __________.
Quadrant III
Quadrant IV
Quadrant I
None of these
Quadrant II
Quadrant III
The graph of the quadratic function is a parabola with its vertex at the point with coordinates
.
Set ; the -coordinate is .
Evaluate by substitution:
The vertex has a negative -coordinate and a negative -coordinate, putting it in the lower left quadrant, or Quadrant III.