Math Problem Statement
Solve and the vertex is -3 1
Solution
To determine the standard form of the quadratic function given the vertex and the values for , , and , we can use the vertex form and convert it to standard form.
Given Data:
- Vertex:
- Values: , ,
Step-by-Step Solution:
-
Vertex Form: The vertex form of a quadratic equation is: where is the vertex. Here, and .
Substituting , , and :
-
Expanding to Standard Form: Now, expand and simplify to get the standard form .
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Conclusion: The standard form of the function is:
So, the values in the question match the equation derived here.
Would you like further explanation on the expansion or on identifying parts of the vertex form?
Related Questions:
- How do you convert from vertex form to standard form for other values of , , and ?
- What does the value of indicate about the parabola's direction and width?
- How can you find the vertex from the standard form of a quadratic equation?
- What role does the value of play in determining the shape of the parabola?
- How do you complete the square to convert from standard form to vertex form?
Tip:
Always double-check each term when expanding squares to avoid small errors, as these can affect the entire equation.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Graphing
Formulas
y = ax^2 + bx + c (Standard form)
Vertex form y = a(x - h)^2 + k
Theorems
Expansion of quadratic expressions
Suitable Grade Level
Grades 9-11
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