Describing the Graph of an Equation
Date: 1/27/96 at 20:35:4 From: Gorav Khanna Subject: graph of an equation Could I please have some help with this question? Thanks... Which of the following is true of the graph of the equation y=2x^2 - 5x + 3 ? A. It is tangent to the x-axis B. It intersects the x-axis at only two distinct points C. It intersects the x-axis at more than two distinct points D. It lies completely below the x-axis E. It lies completely above the x-axis
Date: 4/28/96 at 19:37:37 From: Doctor Steven Subject: Re: graph of an equation We can analyze this to see what we can throw out right away. The parabola opens upward since the coefficient of x^2 is positive so therefore D cannot be true. It is only a second degree equation, so it could not intersect the x-axis more than twice. So C cannot be true. So now we have three choices: A, B, or E. If it's A, then when y = 0 there can only be one value of x that will satisfy the equation. If it's B, then when y = 0, there will be 2 values of x that satisfy the equation. If it's E, then when y = 0, there are no values of x that satisfy the equation. To find out which it is we will set y to zero and look for solutions. So 2x^2 - 5x + 3 = 0. By the quadratic equation we get: x = [5 +- Sqrt(25 - 24)]/4 = [5 +- 1]/4 = 6/4 or 4/4 = 3/2 or 1. There are two values of x which satisfy the equation, so B is the correct answer. Hope this helps. -Doctor Steven, The Math Forum
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