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Question 1000253: In this question, a satellite dish is used as a parabola. This forms a quadratic function. However, the function obtained using experimental data has a b-value in the form y=ax^2+bx+c. Due to the dish being symmetrical in the y-axis, it should not have a b-value. However, I do not understand why the symmetry relates to the b-value.
Answer by josgarithmetic(39630)   (Show Source):
You can put this solution on YOUR website! Begin with the general parabola equation as you have, in that very generalized general form, and use Completing the Square to put the equation into STANDARD FORM, but in doing so, KEEP the same variables with which the equation begins with.
What happens to b?
If the graph is symmetric around the y axis, , then what would this means for b? Note that y=ax^2+bx+c HAS A VERTICAL SYMMETRY AXIS; NOT A HORIZONTAL ONE.
You may want to check about the symbolic steps in this lesson:
Lesson on Completing the Square to Solve a Quadratic Equation.
What is important is how the positioning for measurements were made or defined. We are not told/given where what part of the parabola relates to an Origin for the graph. Is the vertex assigned as ON the origin, or assigned as some other location?
IF the vertex of the satellite dish is located someplace on the y-axis, then b=0. The vertex may then be come c distance up or down, depending on the value of c, but b=0 and this value has no correspondence with the graph; only the c value will do that.
You would have a very generalized standard form equation,
Axis of Symmetry, 
Vertex Point ( -b/(2a), c-b^2/(4a) ).
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