SOLUTION: The graph of{{{ y=3x^2+12x+19 }}} is a parabola that opens in the direction, It has vertex, y-intercep, and real roots.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: The graph of{{{ y=3x^2+12x+19 }}} is a parabola that opens in the direction, It has vertex, y-intercep, and real roots.       Log On


   

Question 366730: The graph of+y=3x%5E2%2B12x%2B19+ is a parabola that opens in the direction, It has vertex, y-intercep, and real roots.


Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
y=3x%5E2%2B12x%2B19
y=3%28x%5E2%2B4x%29%2B19
y=3%28x%5E2%2B4x%2B4%29%2B19-3%284%29
y=3%28x%2B2%29%5E2%2B7
The vertex is (-2,7).
The line of symmetry is x=-2.
The y-intercept is y=19
Since, 3%3E0, the parabola opens upwards.
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3%28x%2B2%29%5E2%2B7=0
3%28x%2B2%29%5E2=-7
%28x%2B2%29%5E2=-%287%2F3%29
This function has no x-intercepts since it has complex roots and doesn't cross the x-axis.
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