Find zeros, max and min classroom.google.com Algebra 1 8.2 Worksheet Characteristics of Quadratic Functions Name Per____Date____ Determine the value of the zeros, the equation of the axis of symmetry, the max or min value and the vertex. 1. 2. 3. Zeros: Axis of symmetry: Max or Min: Vertex: 4 Zeros: Axis of symmetry: Max or Min: Vertex: 5. Zeros: Axis of symmetry: Max or Min: Vertex: 6. Page 1/2 Q
The Correct Answer and Explanation is:
Of course. Here are the correct answers for the first three problems on the worksheet, followed by a detailed explanation of how to find each characteristic from the graphs.
Correct Answers
1.
- Zeros: -4, 0
- Axis of symmetry: x = -2
- Max or Min: Max at 4
- Vertex: (-2, 4)
2.
- Zeros: -5, -1
- Axis of symmetry: x = -3
- Max or Min: Min at -4
- Vertex: (-3, -4)
3.
- Zeros: -3, 3
- Axis of symmetry: x = 0
- Max or Min: Min at -9
- Vertex: (0, -9)
Explanation of Characteristics
This worksheet focuses on identifying the key features of a quadratic function by looking at its graph, which is a parabola. Here is a breakdown of each characteristic and how it was determined for each problem.
Zeros
The zeros of a function, also known as the roots or x-intercepts, are the points where the graph crosses the horizontal x-axis. At these points, the y-value is zero.
- In problem 1, the parabola intersects the x-axis at x = -4 and x = 0.
- In problem 2, the graph crosses the x-axis at x = -5 and x = -1.
- In problem 3, the graph intersects the x-axis at x = -3 and x = 3.
Vertex
The vertex is the turning point of the parabola. It is either the absolute highest point or the absolute lowest point on the graph. The vertex is written as an (x, y) coordinate pair.
- In problem 1, the parabola opens downwards, so the vertex is the highest point, which is located at (-2, 4).
- In problem 2, the parabola opens upwards, making the vertex the lowest point. This point is at (-3, -4).
- In problem 3, the parabola also opens upwards, and its lowest point, the vertex, is at (0, -9).
Axis of Symmetry
The axis of symmetry is a vertical line that divides the parabola into two perfect mirror images. This line always passes through the vertex. The equation for this vertical line is always written as x = c, where ‘c’ is the x-coordinate of the vertex.
- For problem 1, the vertex is at (-2, 4), so the axis of symmetry is the line x = -2.
- For problem 2, the vertex is at (-3, -4), so the axis of symmetry is x = -3.
- For problem 3, the vertex is at (0, -9), meaning the axis of symmetry is the y-axis itself, which has the equation x = 0.
Max or Min Value
A parabola has either a maximum (max) or a minimum (min) value, but never both. This value corresponds to the y-coordinate of the vertex. If the parabola opens downwards like a hill, it has a maximum value. If it opens upwards like a cup, it has a minimum value.
- The parabola in problem 1 opens downwards, so it has a maximum value. The highest y-value it reaches is 4.
- The parabola in problem 2 opens upwards, so it has a minimum value. The lowest y-value it reaches is -4.
- The parabola in problem 3 also opens upwards, so its minimum value is the y-coordinate of its vertex, which is -9.
