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

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

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) (Show Source): You can put this solution on YOUR website!
. 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 (which is really the same thing).

In this equation: , , , and

or
or

To graph the equation, first find the x-coordinate of the vertex given by , then evaluate the function f(x)=y at this x value: . Therefore the vertex is at (1, 1). Since the coefficient on the 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 . , 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.

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
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