Math Problem Statement
Solution
The function given in the image is:
This is a quadratic function, and its graph will be a parabola. Let's break down how to graph it:
Steps to Graph:
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Identify the key features:
- Vertex: The vertex form of a quadratic function is , where is the vertex. You can find the vertex using the formula . Here, and , so: Now, substitute into the equation to find the -coordinate of the vertex: The vertex is at .
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Y-intercept: The y-intercept occurs when : So, the y-intercept is at .
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Axis of Symmetry: The axis of symmetry is the vertical line passing through the vertex, which is .
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Additional Points: To accurately plot the graph, choose other values of , such as and , and compute the corresponding -values:
- For , .
- For , .
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Plot the points:
- Vertex:
- Y-intercept:
- Points: and
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Draw the parabola: Since (positive), the parabola opens upwards. Use the points to sketch a smooth curve.
Would you like further details or help with graphing? Here are some related questions:
- How do you convert a quadratic equation to vertex form?
- How do you determine whether a parabola opens upwards or downwards?
- What is the significance of the axis of symmetry in a quadratic graph?
- How do you find the roots of a quadratic equation?
- How do changes in the coefficients of , , and the constant affect the graph?
Tip: The vertex provides a quick way to know the minimum or maximum point of the parabola, depending on its orientation!
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Math Problem Analysis
Mathematical Concepts
Quadratic Functions
Graphing Parabolas
Algebra
Formulas
Standard form of quadratic function: y = ax^2 + bx + c
Vertex formula: x = -b / (2a)
y-intercept at x = 0
Theorems
Parabolas and Symmetry
Vertex Theorem
Suitable Grade Level
Grades 9-10