Question

Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the domain and range of the function.

A) Axis of symmetry: x = -2, Domain: (-[infinity], [infinity]), Range: [6, [infinity])
B) Axis of symmetry: x = 2, Domain: (-[infinity], [infinity]), Range: (-[infinity], 6]
C) Axis of symmetry: x = -2, Domain: (-[infinity], [infinity]), Range: (-[infinity], 6]
D) Axis of symmetry: x = 2, Domain: (-[infinity], [infinity]), Range: [6, [infinity])

Answer 1

The correct answer is D) Axis of symmetry: x = 2, Domain: (-∞, ∞), Range: [6, ∞). The quadratic function has a vertex at (2, 6), an axis of symmetry at x = 2, and opens upward. The domain spans all real numbers (-∞, ∞), while the range extends from 6 to positive infinity [6, ∞).

Step-by-step explanation:

For a quadratic function in the form
`\( f(x) = ax^2 + bx + c \)`, the axis of symmetry is given by
`\( x = -(b)/(2a) \).` In this case, the axis of symmetry
`\( x = 2 \)`aligns with option D. The function's vertex, determined by the coordinates of the point (h, k), corresponds to the axis of symmetry (h, k). The vertex here is at (2, 6), supporting the chosen answer.

Knowing the axis of symmetry and vertex, the parabola opens upward for a positive leading coefficient, which indicates the range extends from the y-value of the vertex to positive infinity, as confirmed in option D ([6, ∞)). Additionally, the domain of a quadratic function covers all real numbers (-∞, ∞). Therefore, option D accurately represents the properties of the given quadratic function with the correct axis of symmetry, vertex, domain, and range.