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Example Question #51 : Polynomial Functions
How many -intercepts does the graph of the following function have?
Two
One
Ten
Five
Zero
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 #603 : Functions And Graphs
The vertex of the graph of the function
appears in __________.
None of these
Quadrant I
Quadrant IV
Quadrant II
Quadrant III
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 #51 : Polynomial Functions
The vertex of the graph of the function
appears in __________.
None of these
Quadrant IV
Quadrant III
Quadrant II
Quadrant I
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.
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