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6/1
Jan
19
2013
296,541
responses
| Number Answered | |
|---|---|
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32%
correct
Mathematics > Standard Multiple Choice
Read the following SAT test question and then click on a button to select your answer.
In the 
-plane, the graph of the line with equation 
intersects the graph of the quadratic function 
in exactly one point. What is the value of 
?
Hint
If a horizontal line in the 
-plane intersects the graph of a parabola in exactly one point, that point must be the vertex of the parabola.
-plane of the quadratic function 
is a parabola. If the graph of the line with equation 
intersects the graph of this parabola in exactly one point, that point must be the vertex of the parabola, and the 
-coordinate of the point must be 
. The graph of 
intersects the 
-axis at 
and 
, so the 
-coordinate of the vertex of the parabola is halfway between 
and 
on the 
-axis at 
. Thus the 
-coordinate of the vertex is 
. Therefore, if the graph of the line with equation 
intersects the graph of the quadratic function 
in exactly one point, the value of 
must be 
.