Math Problem Statement
Solution
The function given in the image is:
1) What are the zeros of the function?
To find the zeros of the function, set and solve for : This gives us two solutions:
So, the zeros (or roots) of the function are:
- Smaller
- Larger
2) What is the vertex of the parabola?
Since the function is in factored form, we can find the x-coordinate of the vertex as the midpoint of the two zeros:
To find the y-coordinate of the vertex, substitute into the function:
Thus, the vertex of the parabola is:
Would you like further clarification or additional details on any part of this? Below are some follow-up questions for deeper exploration:
- How would the graph of the function look like?
- How can we rewrite the function in standard quadratic form?
- What is the axis of symmetry for this parabola?
- How can you find the y-intercept of this function?
- What does the negative value of the vertex's y-coordinate indicate about the graph?
Tip: The zeros of a quadratic function always help determine where the parabola intersects the x-axis.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Parabolas
Factored Form
Formulas
Zeros of quadratic function: Set each factor equal to zero
Midpoint formula: (x1 + x2) / 2
Evaluate function at x to find y-coordinate
Theorems
Roots of a quadratic equation
Vertex as midpoint of roots for parabolas
Suitable Grade Level
Grades 8-10
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