Question

For the function h(x) = -(x - 5)^2 + 3, what is the vertex, axis of symmetry, y-intercept, and opens direction?

A) Vertex: (5, 3), AOS: x = 5, Y-Int: (0, 8), Opens: Down
B) Vertex: (-5, -3), AOS: x = -5, Y-Int: (0, 8), Opens: Up
C) Vertex: (5, 3), AOS: x = 3, Y-Int: (0, 8), Opens: Down
D) Vertex: (5, 3), AOS: x = 5, Y-Int: (0, 3), Opens: Up

Answer 1

The vertex of the function is (5, 3), the axis of symmetry is x = 5, the y-intercept is (0, 3), and it opens downwards.

Step-by-step explanation:

The function h(x) = -(x - 5)^2 + 3 is in the form of a quadratic function. The vertex of a quadratic function in the form (x - h)^2 + k is represented by the point (h, k). In this case, the vertex is (5, 3), so the answer is option (D).

The axis of symmetry of a quadratic function is a vertical line that passes through the vertex. In this case, the axis of symmetry is x = 5.

The y-intercept is the point where the graph of the function intersects the y-axis. To find the y-intercept, substitute x = 0 into the function. In this case, the y-intercept is (0, 3).

The opens direction of a quadratic function is determined by the sign of the coefficient of the x^2 term. If the coefficient is positive, the graph opens upwards, and if the coefficient is negative, the graph opens downwards. In this case, the coefficient is -1, so the graph opens downwards. Therefore, the correct answer is option (D).