Math Problem Statement
For g(x)=-3x^2+5.2x+7 find the maximum value of the fuction
Solution
To find the maximum value of the quadratic function , we can use the vertex formula. The vertex of a parabola given by a quadratic function occurs at .
Here, the coefficients are:
The x-coordinate of the vertex is:
Next, we substitute this -value back into the original function to find the maximum value:
Let's calculate it step by step:
- Calculate :
- Substitute into the function:
Thus, the maximum value of the function is approximately 9.255.
Would you like further details or have any other questions?
Here are 5 related questions:
- How does the sign of the coefficient in a quadratic function affect the shape of the parabola?
- What is the significance of the vertex in the context of maximizing or minimizing a quadratic function?
- How would the maximum value change if the coefficient of was positive?
- Can you find the roots of the function ?
- How would the function behave as approaches infinity?
Tip: In a quadratic function, if the coefficient of is negative, the parabola opens downward, and the vertex represents the maximum point.
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Math Problem Analysis
Mathematical Concepts
Quadratic Functions
Vertex Formula
Formulas
Vertex formula for quadratic functions
Theorems
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Suitable Grade Level
Grades 10-12