Math Problem Statement

Use the graph of the parabola to fill in the table. (a) Does the parabola open upward or downward? (b) Find the intercept(s). (c) Find the coordinates of the vertex.

Solution

Let's analyze the problem step by step based on the image of the parabola:

  1. Does the parabola open upward or downward?
    From the graph, the parabola opens downward because its arms are facing downwards.

  2. Find the intercepts:

    • x-intercept(s):
      The x-intercepts occur where the parabola crosses the x-axis. From the graph, it crosses at x=2x = -2.

    • y-intercept(s):
      The y-intercept occurs where the parabola crosses the y-axis. From the graph, it crosses at y=1y = -1.

  3. Find the coordinates of the vertex: The vertex is the highest point of the parabola since it opens downward. From the graph, the vertex is located at the point (2,3)(-2, 3).

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Math Problem Analysis

Mathematical Concepts

Quadratic Functions
Parabolas
Vertex
Intercepts

Formulas

Standard form of quadratic equation: y = ax^2 + bx + c
Vertex formula: (-b / 2a, f(-b / 2a))

Theorems

Vertex Theorem
X-Intercept and Y-Intercept properties

Suitable Grade Level

Grades 8-10