Question

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 quadratic
functions 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 1

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 quadratic

functions 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 2

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 quadratic functions and graphing them.

1. If a > 0 (positive), the parabola opens upward. If a 0, it opens downward (negative)

2. The graph of y = ax2 widens when "a" is less and narrows as "a" increases in value. Its axis of symmetry is x = 0, and its vertex is always at the origin (0, 0).

3. To produce the graph of y = ax2 + k, shift y = ax2, k units higher for positive values of k and /k/ units downward for negative values of k. (negative). Its vertex is situated at the intersection of the symmetry axis at (0, k) and x=0.

4. By moving y = ax2, h units to the right if h > 0 (positive), and /h/ units to the left if h 0, the graph of y = a(x - h) is obtained (negative). Its vertex is situated at the intersection of the symmetry axis of x=h and (h, k).

5. The graph of y = a(x-h)2 + k is created by shifting y = ax2, h units upward if k> 0 and /h/ units downward if h > 0 (positive or negative) (positive) and

downward /k/ units if k 0 (negative). Its vertex is situated at the intersection of an axis of symmetry and (h, k).

x= h.

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