Question

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

\\( a < 0 \\)

the vertex is \\( (1,2) \\)

the axis of symmetry is \\( y = 2 \\)

\\( x = 2 \\) is a zero of the function

\\( (1,2) \\) is a minimum

Explanation:

Analyze the direction of opening and leading coefficient \(a\)

$$ \text{The parabola opens downward} \implies a < 0 $$

Identify the vertex and axis of symmetry

$$ \text{Vertex} = (h, k) = (1, 2) $$

$$ \text{Axis of symmetry: } x = 1 $$

$$ \text{Since the parabola opens downward, } (1,2) \text{ is a maximum, not a minimum.} $$

Identify the zeros of the function

$$ \text{The graph intersects the } x\text{-axis at } x = -1 \text{ and } x = 3. $$

$$ x = 2 \text{ is not a zero of the function (the function value at } x=2 \text{ is } 1\text{).} $$

Answer:

• (A) \(a < 0\) (Correct answer)
• (B) The vertex is (1,2) (Correct answer)
• (C) The axis of symmetry is \(y = 2\)
• (D) \(x = 2\) is a zero of the function
• (E) (1,2) is a minimum