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If the function h(x) = ax^2 + bx + c, then how in how many points does the function crosses the X axis
(1) h(x) - 4 crosses the X axis at 2 points
(2) h(x-4) crosses the X axis at 2 points
(1) h(x) - 4 crosses the X axis at 2 points
(2) h(x-4) crosses the X axis at 2 points
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14 Jun 2015, 02:38
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We're graphing a quadratic (assuming a is not zero), which will give us a parabola (a U-shape), so we might have 0, 1 or 2 intersection points with the x-axis.
When you graph any function y = h(x), and then graph y = h(x) - 4, the picture of h(x) - 4 will always be identical to the picture of h(x), except it will be 4 units lower. When we add or subtract a constant to a function, we're just moving the picture up or down. And if you move the picture of a U-shape up or down, you might change the number of intersection points with the x-axis, so Statement 1 is not sufficient.
When you graph a function h(x), and then graph h(x-4), the picture of h(x-4) will be identical to the picture of h(x), except that it will be translated 4 units to the right. That is, when we plug x-k into a function instead of x, we move the function k units to the right. When we move a graph left or right, we don't change how many intersection points we'll get with the x-axis, so Statement 2 is sufficient.
I could explain why graphs move around in that way, but it's not really worth spending time on for the GMAT. I've seen thousands of real GMAT questions, and I've seen exactly one which tests if you know that graphs of functions move up or down when you add a constant on one side of the equation - and that question was much simpler than this one. I've seen zero questions which test if you know that functions move left or right when you plug in (x-k) instead of x. So it's extremely unlikely you'll need to know about this for the test. Where is the question from?
When you graph any function y = h(x), and then graph y = h(x) - 4, the picture of h(x) - 4 will always be identical to the picture of h(x), except it will be 4 units lower. When we add or subtract a constant to a function, we're just moving the picture up or down. And if you move the picture of a U-shape up or down, you might change the number of intersection points with the x-axis, so Statement 1 is not sufficient.
When you graph a function h(x), and then graph h(x-4), the picture of h(x-4) will be identical to the picture of h(x), except that it will be translated 4 units to the right. That is, when we plug x-k into a function instead of x, we move the function k units to the right. When we move a graph left or right, we don't change how many intersection points we'll get with the x-axis, so Statement 2 is sufficient.
I could explain why graphs move around in that way, but it's not really worth spending time on for the GMAT. I've seen thousands of real GMAT questions, and I've seen exactly one which tests if you know that graphs of functions move up or down when you add a constant on one side of the equation - and that question was much simpler than this one. I've seen zero questions which test if you know that functions move left or right when you plug in (x-k) instead of x. So it's extremely unlikely you'll need to know about this for the test. Where is the question from?
14 Jun 2015, 07:49
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Thanks for your explanation. But I found answer I was looking for in the forum
does-g-x-ax-2-bx-c-have-2-intersections-with-axis-x-26775.html?fl=similar
does-g-x-ax-2-bx-c-have-2-intersections-with-axis-x-26775.html?fl=similar
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
