MHB Dstermine the equation of function

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The equation of the axis of symmetry for the quadratic function is x = -1, indicating the vertex form is y = a(x + 1)^2 + k. Using the points (0, 3) and (-3, 9), two equations can be formed to solve for the parameters a and k. The solutions yield two distinct quadratic functions, one with a positive value for a (opening upward) and another with a negative value (opening downward). Both solutions illustrate the nature of parabolas based on the given points and symmetry. The discussion emphasizes the importance of the axis of symmetry in determining the quadratic function's characteristics.
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The equation of the axis of symmetry of the graph of a quadratic function is x=-1. The graph passes through the points (0,3) and (-3, 9). Determine the equation of the function.
 
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$y = a(x-h)^2 + k$

you are given $h = -1$

write two equations using the two given (x,y) coordinates and solve the system for $a$ and $k$
 
Azurin said:
The equation of the axis of symmetry of the graph of a quadratic function is x=-1. The graph passes through the points (0,3) and (-3, 9). Determine the equation of the function.
Actually, there are two solutions... one with a = A and one with a = -A. This corresponds to one parabola opening upward and another opening downward.

-Dan
 

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