Math Problem Statement

f(x) = -1/2x^2 + 4x + 5

Solution

The function provided in the image is:

f(x)=−12x2+4x+5f(x) = -\frac{1}{2}x^2 + 4x + 5

How can I assist you with this function? For example, I can:

  1. Find the vertex of the parabola (maximum point, since it opens downward).
  2. Determine the roots (x-intercepts) using the quadratic formula.
  3. Identify the y-intercept.
  4. Analyze its domain and range.
  5. Plot the graph of the function.

Let me know which analysis you'd like, or if you'd like detailed solutions!

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Math Problem Analysis

Mathematical Concepts

Quadratic Functions
Parabolas
Vertex and Roots Analysis

Formulas

Vertex formula: x = -b/(2a)
Quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
General form of a quadratic equation: ax^2 + bx + c

Theorems

Properties of parabolas
Discriminant analysis for roots

Suitable Grade Level

Grades 8-10

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