Question of the Day

Can you answer today's question?

Register Next Tests:
5/3 , 6/7

http://sat.collegeboard.org/practice/sat-question-of-the-day
Apr
19
Question of the Day Statistics
Number Answered
Correct 13,052
Incorrect 27,954
41,006 responses
31% correct
See Last Thirty Questions:

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

Correct!

Explanation

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.

Log in, track your progress and review questions.
Want to brush up on your skills? Just visit our Practice Questions area.

Buy Together, Get $10 Off

Buy Together & Get $10 Off
Study Guide
Online Course

The online course includes explanations and auto essay scoring for the Study Guide's 10 practice tests.

The Official Study Guide for All SAT Subject Tests™: 
Second Edition

Subject Test Study Guide

Get ready for test day with a brand new edition of our best-selling SAT Subject Test Study Guide! Brought to you by the test-maker, this is the ONLY study guide with actual, previously administered tests for all 20 SAT Subjects Tests™ to provide you with the real test-taking experience.

See Inside