Math Problem Statement
Consider the graph of the quadratic function f(x) = −3(x − 2)2 − 4 to complete the statement.
The graph of the function f(x) = −3(x − 2)2 − 4 has a ____ value of .
Solution
The given quadratic function is:
This is in vertex form, , where:
- (indicating the parabola opens downwards because is negative)
- (the x-coordinate of the vertex)
- (the y-coordinate of the vertex)
Since the parabola opens downward, the vertex represents the maximum point of the graph.
Thus, the graph of the function has a maximum value of -4.
Would you like more details or have any other questions?
Here are some related questions for further practice:
- What is the vertex of the quadratic function ?
- How does the value of affect the shape and direction of a parabola?
- What is the axis of symmetry for the function ?
- How would you determine the x-intercepts of a quadratic function?
- How do you convert a quadratic function from standard form to vertex form?
Tip: The vertex form of a quadratic function makes it easy to identify the maximum or minimum value directly.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Quadratic Functions
Vertex Form of a Quadratic
Graphing Parabolas
Formulas
Vertex Form: f(x) = a(x - h)² + k
Maximum or Minimum Value of a Parabola
Theorems
A parabola opens downward if the coefficient a < 0, and the vertex represents the maximum value.
Suitable Grade Level
Grades 9-11