Question

Consider the graph of the function F(x)=2(x-3)^2-4

Answer 1

The graph of the quadratic function
`\(f(x) = 2(x - 3)^2 - 4\)` reveals a vertex at (3, -4), an axis of symmetry at x = 3, and additional points obtained by reflection across the axis.

A. Plot the vertex:

- The given function is in vertex form, f(x) = a(x - h)^2 + k, where (h, k) is the vertex.

- For
`\(f(x) = 2(x - 3)^2 - 4\)`, the vertex is (3, -4). Plot this point.

B. Graph the axis of symmetry using two points other than the vertex:

- The axis of symmetry for a parabola in the form
`\(y = a(x - h)^2 + k\)` is the vertical line x = h.

- Choose two points on either side of the vertex and draw a line through them. This line is the axis of symmetry.

C. Plot the point with x-coordinate 1 less than that of the vertex:

- The x-coordinate is 3 - 1 = 2. So, the point is (2, f(2)).

D. Plot the point with x-coordinate 2 less than that of the vertex:

- The x-coordinate is 3 - 2 = 1. So, the point is (1, f(1)).

E. Reflect the plotted points in the axis of symmetry:

- Reflect points (2, f(2)) and (1, f(1)) across the axis of symmetry (x = 3) to obtain two more points.

Now, connect these points to sketch the graph of the function f(x) = 2(x - 3)^2 - 4.

The probable question may be:

Consider the graph of the function f(x) = 2(x-3)^2 -4.

A Plot the vertex.

B Graph the axis of symmetry using two points other than the vertex.

C Plot the point on the graph whose x-coordinate is 1 less than that of the vertex.

D Plot the point on the graph whose x-coordinate is 2 less than that of the vertex.

E Reflect the plotted points in the axis of symmetry to plot two more points on the graph.