Identify key features of quadratic functions from their graphs.

Let's analyze each quadratic graph one by one and identify the key features: x-intercepts, y-intercept, vertex, point of extremum (maximum or minimum), axis of symmetry, roots, solutions, and zeros.

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🔷 Graph 1

#### Graph Description:
- Parabola opens downward (so it has a maximum).
- Vertex at (1, 4).
- Crosses x-axis at x = -1 and x = 3.
- Crosses y-axis at y = 3.
- Axis of symmetry is halfway between the x-intercepts: $ x = \frac{-1 + 3}{2} = 1 $.

#### ✔ Key Features:

- X-Intercept(s): $ x = -1 $ and $ x = 3 $
- Y-Intercept: $ y = 3 $
- Vertex: $ (1, 4) $
- Point of Extremum: Maximum, $ y = 4 $
- Axis of Symmetry: $ x = 1 $
- Root(s): $ x = -1 $, $ x = 3 $
- Solution(s): $ x = -1 $, $ x = 3 $
- Zero(s): $ x = -1 $, $ x = 3 $

> Note: Roots, Solutions, and Zeros are all the same in this context — they refer to the x-values where the function equals zero.

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🔷 Graph 2

#### Graph Description:
- Parabola opens downward → maximum.
- Vertex at (-1, 2).
- Crosses x-axis at x = -3 and x = 1.
- Crosses y-axis at y = -4.
- Axis of symmetry: midpoint of $-3$ and $1$: $ x = \frac{-3+1}{2} = -1 $

#### ✔ Key Features:

- X-Intercept(s): $ x = -3 $, $ x = 1 $
- Y-Intercept: $ y = -4 $
- Vertex: $ (-1, 2) $
- Point of Extremum: Maximum, $ y = 2 $
- Axis of Symmetry: $ x = -1 $
- Root(s): $ x = -3 $, $ x = 1 $
- Solution(s): $ x = -3 $, $ x = 1 $
- Zero(s): $ x = -3 $, $ x = 1 $

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🔷 Graph 3

#### Graph Description:
- Parabola opens downward → maximum.
- Vertex at (-2, 4).
- Crosses x-axis at x = -4 and x = 0.
- Crosses y-axis at y = 0 (since it passes through origin).
- Axis of symmetry: $ x = \frac{-4 + 0}{2} = -2 $

#### ✔ Key Features:

- X-Intercept(s): $ x = -4 $, $ x = 0 $
- Y-Intercept: $ y = 0 $
- Vertex: $ (-2, 4) $
- Point of Extremum: Maximum, $ y = 4 $
- Axis of Symmetry: $ x = -2 $
- Root(s): $ x = -4 $, $ x = 0 $
- Solution(s): $ x = -4 $, $ x = 0 $
- Zero(s): $ x = -4 $, $ x = 0 $

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✔ Final Answer Summary

#### Graph 1
- X-Intercept(s): $ x = -1, 3 $
- Y-Intercept: $ y = 3 $
- Vertex: $ (1, 4) $
- Point of Extremum: Maximum, $ y = 4 $
- Axis of Symmetry: $ x = 1 $
- Root(s): $ x = -1, 3 $
- Solution(s): $ x = -1, 3 $
- Zero(s): $ x = -1, 3 $

#### Graph 2
- X-Intercept(s): $ x = -3, 1 $
- Y-Intercept: $ y = -4 $
- Vertex: $ (-1, 2) $
- Point of Extremum: Maximum, $ y = 2 $
- Axis of Symmetry: $ x = -1 $
- Root(s): $ x = -3, 1 $
- Solution(s): $ x = -3, 1 $
- Zero(s): $ x = -3, 1 $

#### Graph 3
- X-Intercept(s): $ x = -4, 0 $
- Y-Intercept: $ y = 0 $
- Vertex: $ (-2, 4) $
- Point of Extremum: Maximum, $ y = 4 $
- Axis of Symmetry: $ x = -2 $
- Root(s): $ x = -4, 0 $
- Solution(s): $ x = -4, 0 $
- Zero(s): $ x = -4, 0 $

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📝 Notes:

- All three parabolas open downward, so they have maximums.
- The vertex is always the highest point.
- Axis of symmetry is the vertical line through the vertex.
- X-intercepts, roots, solutions, and zeros are all synonymous here — they are the values of $ x $ where $ y = 0 $.
- Y-intercept is where $ x = 0 $.

Let me know if you'd like the equations of the quadratics as well!