Math Problem Statement
What is the range of this quadratic function?
y
=
–
x
2
–
2
x
8
Solution
To find the range of the quadratic function , let's go through the steps:
1. Identify the vertex of the parabola:
The function is in the form , where , , and .
The x-coordinate of the vertex is calculated using the formula: Substituting the values of and :
2. Find the y-coordinate of the vertex:
Substitute back into the equation to find :
3. Determine the range:
Since the coefficient of (which is ) is negative, the parabola opens downward. This means the vertex is the maximum point.
Therefore, the range of the function is:
Would you like more details or have any questions?
5 Related Questions:
- How do you find the x-intercepts of a quadratic function?
- What is the significance of the vertex in determining the maximum or minimum value?
- How can you convert a quadratic function to vertex form?
- How does the value of in the quadratic function affect the graph?
- What is the relationship between the axis of symmetry and the vertex?
Tip:
The range of a quadratic function depends on whether the parabola opens upward or downward. The vertex provides the highest or lowest point, which helps determine the range.
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Math Problem Analysis
Mathematical Concepts
Quadratic Functions
Vertex of a Parabola
Range of Functions
Formulas
Vertex formula: x = -b/(2a)
Quadratic function: y = ax^2 + bx + c
Theorems
Maximum/Minimum Value Theorem for Quadratic Functions
Suitable Grade Level
Grades 10-12
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