Math Problem Statement
Write the quadratic function that goes through the points (0,8) (2,18) (3,17)
Solution
To find a quadratic function that passes through the points , , and , we can use the fact that each point will satisfy this function, giving us a system of equations for , , and .
Step 1: Set up equations
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Using the point :
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Using the point : Substituting :
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Using the point : Substituting :
Step 2: Solve the system of equations for and
We now have two equations:
Subtract the first equation from the second:
Substitute into the first equation:
Step 3: Write the quadratic function
We found that , , and . So, the quadratic function is:
Final Answer:
Would you like to go over the verification or any specific details?
- How can we verify that the function passes through each point?
- What other forms can a quadratic function take?
- How does changing , , or affect the shape of the graph?
- How do we find the vertex of this quadratic function?
- Can this quadratic function have real roots?
Tip: To confirm if a quadratic function fits specific points, plug each point into the function to see if the resulting equations hold true.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Systems of Linear Equations
Formulas
Quadratic function f(x) = ax^2 + bx + c
Substitution to solve systems of equations
Theorems
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Suitable Grade Level
Grades 10-12
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