For \(g(x)=-(x+1)^{2}+4\), give the vertex, symmetry axis, opening, scale, and extremum. Evaluate two inputs equally spaced from the axis and state the resulting symmetric points.

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The vertex is (−1, 4) and g(−2) = g(0) = −1. Substituting either input gives 3.

The vertex is (1, 4), with axis x = 1. Since x + 1 = x − (−1), the axis is x = −1.

The vertex is (−1, 4), axis x = −1, and the parabola opens down with parent-function width. It has maximum 4; g(−2) = g(0) = 3, giving symmetric points (−2, 3) and (0, 3).

The vertex is (−1, 4) and the parabola opens up with minimum 4. The leading negative reflects it down.

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Curriculum context

Course: Math II
Standard: A-SSE.3.b
Category: Algebra
Domain: Seeing Structure in Expressions
Objective: Complete the square to reveal maximum or minimum values of quadratic functions.
Problem type: Extract graph features from completed-square form