Math Problem Statement
What is the vertex of the function?
f(x)=4x2+8x+3
Solution
To find the vertex of a quadratic function of the form , we use the vertex formula:
For the given function , we have:
Let's calculate the -coordinate of the vertex:
Now, substitute back into the function to find the -coordinate:
So, the vertex is .
The vertex of the function is .
Would you like more details or have any questions?
Here are 5 related questions to expand your understanding:
- How do you find the axis of symmetry for a quadratic function?
- What is the significance of the vertex in a quadratic function?
- How does the coefficient of affect the direction of the parabola?
- Can you rewrite the quadratic function in vertex form?
- How do you find the intercepts of a quadratic function?
Tip: The vertex form of a quadratic function, , makes it easier to identify the vertex and graph the function.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Vertex of a Parabola
Formulas
Vertex formula: x = -b / 2a
Quadratic function: f(x) = ax^2 + bx + c
Theorems
Vertex Theorem for Quadratic Functions
Suitable Grade Level
Grades 9-11