Question

Graph the function f(x)=6x^2–7.
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.

Answer 1

1. Find the vertex:
- f(x) = 6x^2 − 7 has a = 6, b = 0, c = −7.
- Vertex x = −b/(2a) = 0, so vertex = (0, −7). Plot that point.

2. Plot another point on the parabola:
- Choose x = 1: f(1) = 6(1)^2 − 7 = −1 → point (1, −1). Plot that.
- (Optionally also plot the symmetric point (−1, −1) for a better shape.)

3. Additional helpful points (for sketching):
- x = −2 → f = 17 → (−2, 17)
- x = −1 → f = −1 → (−1, −1)
- x = 0 → f = −7 → (0, −7) (vertex)
- x = 1 → f = −1 → (1, −1)
- x = 2 → f = 17 → (2, 17)

4. Draw the parabola:
- It opens upward (a = 6 > 0). Smoothly connect the plotted points in a U-shape, symmetric about the vertical line x = 0 (the axis of symmetry).

5. To erase and restart:
- Select the second point and drag it on top of the first (place (1, −1) on top of (0, −7)); that will remove the drawn parabola so you can place a different second point.

That’s all you need to graph f(x)=6x^2−7 and correct mistakes.