Question #1697ffcf - SAT Suite Question Bank

ID: 1697ffcf

Modded SAT Question Bank by Abdullah Mallik

In the xy-plane, the graph of $y equals 3 x squared minus 14 x$ intersects the graph of $y equals x$ at the points $with coordinates zero comma zero$ and $a, comma a$ . What is the value of a ?

Toggle Answer

Tip: Press CTRL/Command to toggle answer

Correct Answer:

Rationale

The correct answer is 5. The intersection points of the graphs of $y equals, 3 x squared, minus 14 x$ and $y equals x$ can be found by solving the system consisting of these two equations. To solve the system, substitute x for y in the first equation. This gives $x equals, 3 x squared, minus 14 x$ . Subtracting x from both sides of the equation gives $0 equals, 3 x squared, minus 15 x$ . Factoring $3 x$ out of each term on the left-hand side of the equation gives $0 equals, 3 x times, open parenthesis, x minus 5, close parenthesis$ . Therefore, the possible values for x are 0 and 5. Since $y equals x$ , the two intersection points are $the points with coordinates 0 comma 0$ and $5 comma 5$ . Therefore, $a, equals 5$ .

Question Difficulty: Hard