Quadratic Functions: Vertex Form Answers

If h = 3, the vertex shifts to .

(–5, 0)(0, –5)(0, 5)(5, 0)

Graph h(x) = 0.5(x + 2)^2 − 4 by following these steps: | Steps: Step 1: Identify a, h, and k. | Step 1: | Step 2: Plot the vertex at (−2, −4). | Step 2: | Step 3: The axis of symmetry is the line | Step 3: | Step 4: Evaluate the function at two other x-values: | Step 4: | Step 5: Plot the points (−4, −2) and (−6, 4). | Step 5: | Step 6: Use the property of symmetry to plot two more corresponding points on the right side of the vertical line. | Step 6: | Step 7: The smooth curve through these points shows the graph of the function. | Step 7: | [=]

Graph h(x) = 0.5(x + 2)^2 − 4 by following these steps: | Steps: Step 1: Identify a, h, and k. | Step 1: | Step 2: Plot the vertex at (−2, −4). | Step 2: | Step 3: The axis of symmetry is the line | Step 3: | Step 4: Evaluate the function at two other x-values: | Step 4: | Step 5: Plot the points (−4, −2) and (−6, 4). | Step 5: | Step 6: Use the property of symmetry to plot two more corresponding points on the right side of the vertical line. | Step 6: | Step 7: The smooth curve through these points shows the graph of the function. | Step 7: | [=]

Graph h(x) = 0.5(x + 2)^2 − 4 by following these steps: | Steps: Step 1: Identify a, h, and k. | Step 1: | Step 2: Plot the vertex at (−2, −4). | Step 2: | Step 3: The axis of symmetry is the line | Step 3: | Step 4: Evaluate the function at two other x-values: | Step 4: | Step 5: Plot the points (−4, −2) and (−6, 4). | Step 5: | Step 6: Use the property of symmetry to plot two more corresponding points on the right side of the vertical line. | Step 6: | Step 7: The smooth curve through these points shows the graph of the function. | Step 7: | [(−4) =]

Graph h(x) = 0.5(x + 2)^2 − 4 by following these steps: | Steps: Step 1: Identify a, h, and k. | Step 1: | Step 2: Plot the vertex at (−2, −4). | Step 2: | Step 3: The axis of symmetry is the line | Step 3: | Step 4: Evaluate the function at two other x-values: | Step 4: | Step 5: Plot the points (−4, −2) and (−6, 4). | Step 5: | Step 6: Use the property of symmetry to plot two more corresponding points on the right side of the vertical line. | Step 6: | Step 7: The smooth curve through these points shows the graph of the function. | Step 7: | [(−6) =]

Positive values of k shift the graph .

The function f(x) = –0.3(x – 5)2 + 5 is graphed. What are some of its key features? Check all that apply.

Graph h(x) = 0.5(x + 2)^2 − 4 by following these steps: | Steps: Step 1: Identify a, h, and k. | Step 1: | Step 2: Plot the vertex at (−2, −4). | Step 2: | Step 3: The axis of symmetry is the line | Step 3: | Step 4: Evaluate the function at two other x-values: | Step 4: | Step 5: Plot the points (−4, −2) and (−6, 4). | Step 5: | Step 6: Use the property of symmetry to plot two more corresponding points on the right side of the vertical line. | Step 6: | Step 7: The smooth curve through these points shows the graph of the function. | Step 7: | [=]

Negative values of k shift the graph .

Graph h(x) = 0.5(x + 2)^2 − 4 by following these steps: | Steps: Step 1: Identify a, h, and k. | Step 1: | Step 2: Plot the vertex at (−2, −4). | Step 2: | Step 3: The axis of symmetry is the line | Step 3: | Step 4: Evaluate the function at two other x-values: | Step 4: | Step 5: Plot the points (−4, −2) and (−6, 4). | Step 5: | Step 6: Use the property of symmetry to plot two more corresponding points on the right side of the vertical line. | Step 6: | Step 7: The smooth curve through these points shows the graph of the function. | Step 7: | [=]