Chapter Closure
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Line of Symmetry: x_s=- 4
Line of Symmetry: x_s=- 4
Line of Symmetry: x_s=3
Function:& y=a(x-( -4))^2+ 3 Vertex:& ( -4, 3) To complete the equation, we need the value of a. To do this, we would need to know a second point that falls on the parabola. However in this case, we are free to choose the vertical stretch as long as the parabola opens upward. This will happen as long as a is positive. Let's make our life easy and choose a= 1. y= 1(x-(-4))^2+3 ⇕ y=(x+4)^2+3 The parabola's line of symmetry is a vertical line through its vertex. Therefore, we know that the line of symmetry is x_s=-4.
To make the parabola open downward, we have to choose a to be less than 0. Also, to compress the parabola, the value of a must fall between 0 and -1. We can for example choose a= -0.5. y= - 0.5 (x+4)^2+3 Since the factors of h and k are the same, the line of symmetry will not change.
Finally, to vertically stretch the function, we have to decrease the value of a from -0.5 until its less than -1. This makes it thinner than the original parabola from Part A. We could for example choose a=-2.
The vertex is at x=3 and therefore the line of symmetry is x_s=3.