Question

What are the features of the quadratic function graphed in the figure?

A) Vertex = (–3,4), y-intercept = (0,–5), x-intercepts = (–5,0) and (–1,0), axis of symmetry is x = –3

B) Vertex = (3,–4), y-intercepts = (–1,0) and (–5,0), x-intercept = (0,5), axis of symmetry is x = 3

C) Vertex = (–3,4), y-intercept = (0,–5), x-intercepts = (1,0) and (5,0), axis of symmetry is x = –3

D)Vertex = (–4,3), y-intercept = (5,0), x-intercepts = (0,1) and (0,5), axis of symmetry is x = –4

Answer 1

A) Vertex = (-3, 4), y-intercept = (0, -5), x-intercepts = (-5, 0) and (-1, 0), axis of symmetry is x = -3

Explanation:

The vertex of a quadratic function is the turning point. As this parabola opens downwards, the vertex is the maximum point of the graph. From inspection of the graph, the maximum point is at (-3, 4). Therefore:

• The vertex of the quadratic function is (-3, 4).

The y-intercept is the point at which the curve crosses the y-axis. From inspection of the graph, the curve crosses the y-axis at y = -5. Therefore:

• The y-intercept of the quadratic function is (0, -5).

The x-intercepts are the points at which the curve crosses the x-axis. From inspection of the graph, the curve crosses the x-axis at x = -5 and x = -1. Therefore:

• The x-intercepts of the quadratic function are (-5, 0) and (-1, 0).

The axis of symmetry is the vertical line that passes through the vertex of the parabola so that the left and right sides of the parabola are symmetrical. So the axis of symmetry is the x-value of the vertex. Therefore:

• The axis of symmetry of the quadratic function is x = -3.