Find the vertex and axis of symmetry, and then graph the parabola given by:

Question

Quizplus · Accepted Answer

To find the vertex and axis of symmetry of a parabola in the standard form y = a(x-h)^2 + k, we simply look at the values of h and k.

For choice A, h = -9 and k = 14, so the vertex is (h,k) = (-9,14) and the axis of symmetry is x = -9. However, the given equation has imaginary roots, indicating that it does not intersect the x-axis and therefore cannot be graphed as a parabola.

For choice B, h = 8 and k = -23, so the vertex is (h,k) = (8,-23) and the axis of symmetry is x = 8. This parabola opens upward, so its lowest point is the vertex. However, without additional information about the value of a, we cannot determine the exact shape or steepness of the curve.

For choice C, h = -7/8 and k = -9/16, so the vertex is (h,k) = (-7/8,-9/16) and the axis of symmetry is x = -7/8. This parabola opens upward and is very narrow, indicating that a is a large positive value. We can also see that the parabola intersects the x-axis at two distinct points, suggesting that it has real roots and can be graphed as a parabola.

Therefore, choice C is the best option.

Find the Vertex and Axis of Symmetry, and Then Graph