the graph of a quadratic function is shown. check all of the following statements that are true of the…

Explanation:

Step1: Analyze the coefficient (a)

For a quadratic function (y = ax^{2}+bx + c), if the parabola opens down - ward, (a<0). The given parabola opens down - ward, so (a < 0) is True.

Step2: Identify the vertex

The vertex of a parabola is the maximum or minimum point. For the given parabola, the highest point (since it opens down - ward) is ((1,2)). So, the vertex is ((1,2)) is True.

Step3: Determine the axis of symmetry

The axis of symmetry of a parabola (y = ax^{2}+bx + c) is given by the formula (x=-\frac{b}{2a}). For a parabola with vertex ((h,k)), the axis of symmetry is (x = h). Here, (h = 1), so the axis of symmetry is (x = 1), not (y = 2). So, the axis of symmetry is (y = 2) is False.

Step4: Check the zero of the function

A zero of the function is a value of (x) for which (y = 0). When (x = 2), (y\neq0). So, (x = 2) is a zero of the function is False.

Step5: Classify the vertex

Since the parabola opens down - ward, the vertex ((1,2)) is a maximum (not a minimum). So, ((1,2)) is a minimum is False.

Answer:

• (a<0)
• The vertex is ((1,2))