SOLUTION: 1.For each quadratic function, state: direction of opening, vertex, equation of axis of symmetry, coordinates of maximum or minimum and domain and range.
(a)y=-2x^2-3
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Question 322171: 1.For each quadratic function, state: direction of opening, vertex, equation of axis of symmetry, coordinates of maximum or minimum and domain and range.
(a)y=-2x^2-3
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The lead coefficient is positive, so it opens up.
There is no 1st degree term, so the vertex is the 
-axis. Therefore the value of the 
-coordinate of the vertex is 0 and the value of the function when is zero is \ =\ -2(0)^2\ -\ 3\ =\ -3)
, hence the vertex is at the point )
.
The axis of symmetry is the vertical line passing through the vertex. The equation of any vertical line is 
where 
is the -coordinate of any point on the line. Since we know the vertex is on the line and we have already determined that the -coordinate of the vertex is 0...
The parabola opens upward, so the vertex is a minimum.
The domain of any polynomial function with real-valued coefficients is the set of real numbers.
The range of a parabola that opens upward is 
where 
is the -coordinate of the vertex.
John
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