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Graph the function f(x)=7(x–2)2+1.

Plot the vertex. Then plot another point on the parabola. If you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.

1 answer

To graph the function \( f(x) = 7(x - 2)^2 + 1 \), we need to identify its vertex and another point on the parabola.

  1. Vertex: The vertex form of a quadratic function is given by \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex. In your case:

    • \( a = 7 \)
    • \( h = 2 \)
    • \( k = 1 \)

    Thus, the vertex is located at the point \( (2, 1) \).

  2. Another Point: To find another point on the parabola, we can choose a value for \( x \) other than 2. Let's choose \( x = 3 \): \[ f(3) = 7(3 - 2)^2 + 1 = 7(1)^2 + 1 = 7 + 1 = 8. \] So, the point \( (3, 8) \) lies on the parabola.

  3. Plotting:

    • Plot the vertex \( (2, 1) \).
    • Plot the point \( (3, 8) \).
    • The parabola opens upwards because \( a = 7 > 0 \).

  4. Graphing the Parabola:

    • The general shape of the parabola can be sketched through its vertex and the additional point.
    • Since we already have the vertex and another point, we can reflect across the axis of symmetry \( x = 2 \) to find more points if needed (for example, the point \( (1, 8) \) symmetric to point \( (3, 8) \)).

Based on these steps, your parabola should be properly plotted with the vertex at \( (2, 1) \) and another point at \( (3, 8) \).