SOLUTION: I need help finding the X and Y intercepts and vertex of Y=3X^2-6X-5

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Question 539861: I need help finding the X and Y intercepts and vertex of Y=3X^2-6X-5
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Y=3X%5E2-6X-5 intercept the y-axis (which is the X=0 line)
at Y=-5. So the y-intercept is the point is (0,-5).
Because 3%28X-1%29%5E2-8=3%28x%5E2-2x%2B1%29-8=3X%5E2-6X%2B3-8=3X%5E2-6X-5,
The equation can be re-written as
Y=3%28X-1%29%5E2-8,
showing that the vertex is the point with X=1 and Y=-8.
So the vertex is the point (1,-8).
The x-intercepts are the points where the parabola crosses the x-axis (which is the Y=0 line).
At those points, substituting Y=0 in the modified equation, we see that
0=3%28X-1%29%5E2-8 <--> 3%28X-1%29%5E2=8 <--> %28X-1%29%5E2=8%2F3
That gives us two solutions
X-1=sqrt%288%2F3%29 and X-1=sqrt%288%2F3%29
or X=1+%2B-+sqrt%288%2F3%29
Multiplying and dividing by 6 we get a more popular way of expressing the solutions, which can be further simplified
X=%286%2B-+sqrt%2896%29%29%2F6=%286%2B-+4sqrt%286%29%29%2F6=%283%2B-+2sqrt%286%29%29%2F3
The x-intercepts are the points with the above values for x and Y=0.