What happened to the movement if the graph as the value of h was changed from positive 3 into negative 3 in graph 2?
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Answer:
B. Show the following effects of the changing values of a, h and k in the equation y = a[x - h} + k of a quadratic function by formulating your own quadraticfunctions and graphing it.1. The parabola opens upward if a >0 (positive) and opens downward if a<0 (negative)2. The graph of y = ax2 narrows if the value of "a" becomes larger and widens when the value of "a" is smaller. Its vertex is always located at the origin (0,0) and the axis of symmetry is x = 0.3. The graph of y = ax2 + k is obtained by shifting y = ax2, k units upward if k > 0 (positive) and /k/ units downward if k <0(negative). Its vertex is located at the point of (0, k) and an axis of symmetry of x=0.4. The graph of y = a(x - h) is obtained by shifting y = ax2, h units to the right if h > 0 (positive) and /h/ units to the left if h <0(negative). Its vertex is located at the point of (h, k) and an axis of symmetry of x= h.5. The graph of y = a(x-h)2 + k is obtained by shifting y = ax2, h units to the right if h > 0(positive) /h/ units to the left if h <0(negative); and k units upward if k> 0 (positive) and /k/ units downward if k <0(negative). Its vertex is located at the point of (h, k) and an axis of symmetry of x= h.
Answer · 26 votes
Answer:B. Show the following effects of the changing values of a, h and k in the equation y = a[x - h} + k of a quadratic function by formulating your own quadraticfunctions and graphing it.1. The parabola opens upward if a >0 (positive) and opens downward if a<0 (negative)2. The graph of y = ax2 narrows if the value of "a" becomes larger and widens when the value of "a" is smaller. Its vertex is always located at the origin (0,0) and the axis of symmetry is x = 0.3. The graph of y = ax2 + k is obtained by shifting y = ax2, k units upward if k > 0 (positive) and /k/ units downward if k <0(negative). Its vertex is located at the point of (0, k) and an axis of symmetry of x=0.4. The graph of y = a(x - h) is obtained by shifting y = ax2, h units to the right if h > 0 (positive) and /h/ units to the left if h <0(negative). Its vertex is located at the point of (h, k) and an axis of symmetry of x= h.5. The graph of y = a(x-h)2 + k is obtained by shifting y = ax2, h units to the right if h >…...
Why does a positive value of h shift a graph to the left and not the right?
Answer · 6 votes
You can visualise this easily. [math]y = f(x+h) [/math] Now if the argument of the function is taken as [math](x-h)[/math] the value of y will be [math]f((x-h) + h ) = f(x)[/math] What do you see then ? The function [math]y[/math] acquires the value of [math]f(x)[/math] at [math](x-h)[/math] amounting to a left shift. image source : Gnuplot %3E The green graph is the shifted function. Hope this makes things clear. All I did was demonstrate the[math] f(x-h)[/math] reaches the value f(x) reach[math] h[/math] units ago.