SOLUTION: I have tried to do this equation but I'm having trouble with it. Can you please help me? Solve and graph the equation. y= -3x^2 + 6x - 2

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I have tried to do this equation but I'm having trouble with it. Can you please help me? Solve and graph the equation. y= -3x^2 + 6x - 2      Log On


   

Question 116123This question is from textbook Introductry Algebra
: I have tried to do this equation but I'm having trouble with it. Can you please help me? Solve and graph the equation.
y= -3x^2 + 6x - 2 This question is from textbook Introductry Algebra

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
y=+-3x%5E2+%2B+6x+-+2. By 'solve' I presume you mean to find the roots of the equation where y = 0.

Since this cannot be factored, you must either complete the square or use the quadratic formula x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+(which is really the same thing).

In this equation: -3x%5E2+%2B+6x+-+2=0, a=-3, b=6, and c=-2

x+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A%28-3%29%2A%28-2%29+%29%29%2F%282%2A%28-3%29%29+

x=+%28-6+%2B-+sqrt%2812%29%29%2F%28-6%29

x=%28-6%2B2sqrt%283%29%29%2F-6 or x=%28-6-2sqrt%283%29%29%2F-6
x=%283-sqrt%283%29%29%2F3 or x=%283%2Bsqrt%283%29%29%2F3

To graph the equation, first find the x-coordinate of the vertex given by -b%2F2a=-6%2F-6=1, then evaluate the function f(x)=y at this x value: f%281%29=-3%2B6-2=1. Therefore the vertex is at (1, 1). Since the coefficient on the x%5E2 term is negative, you know the graph is convex down. With the vertex at (1,1), we have an axis of symmetry at the vertical line x=1. f%280%29=0%2B0-2=-2, so we have the y-axis intercept at (0,-2). The roots of the equation that we calculated above come out to a little less than .5 for one and a little more than 1.5 for the other. That's close enough for graphing purposes. If you want to pick a few more values for x to give you some additional points to smooth the curve, pick them in the neighborhood of .5 and 1.5. Plot all of these points and then draw a smooth curve.

graph%28600%2C600%2C-5%2C5%2C-5%2C5%2C-3x%5E2%2B6x-2%29

Super-Double-Plus Extra Credit: Why did I say that using the quadratic formula and completing the square are really the same thing?

Hope that helps,
John