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Apr
19
2014
12,287 responses
Question of the Day Statistics
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Correct 3,918
Incorrect 8,369
31% correct

Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

In the xy -plane, the graph of the line with equation y equals a intersects the graph of the quadratic function (f times x) equals x^2 minus (6 times x) plus 8 in exactly one point. What is the value of a?

Answer Choices

Hint

If a horizontal line in the xy -plane intersects the graph of a parabola in exactly one point, that point must be the vertex of the parabola.

Question of the Day

Can you answer today's question?

Register Next Tests:
5/3 , 6/7

Apr
19
2014
12,287 responses
Question of the Day Statistics
Number Answered
Correct 3,918
Incorrect 8,369
31% correct

Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

In the xy -plane, the graph of the line with equation y equals a intersects the graph of the quadratic function (f times x) equals x^2 minus (6 times x) plus 8 in exactly one point. What is the value of a?

Answer Choices

Answer

The graph in the xy -plane of the quadratic function f time x = (x^2) minus (6 times x) plus 8 is a parabola. If the graph of the line with equation y equals a intersects the graph of this parabola in exactly one point, that point must be the vertex of the parabola, and the y -coordinate of the point must be a. The graph of (f times x) equals (x^2) minus (6 times x) plus 8 equals ((x minus 2) times (x minus 4)) intersects the x -axis at x equals 2 and x equals 4, so the x -coordinate of the vertex of the parabola is halfway between x equals 2 and x equals 4 on the x -axis at x equals 3. Thus the y -coordinate of the vertex is (f times 3) equals (3^2) minus (6 times 3) plus 8 equals -1. Therefore, if the graph of the line with equation y equals a intersects the graph of the quadratic function (f times x) equals (x^2) minus (6 times x) plus 8 in exactly one point, the value of a must be negative 1.