Math Problem Statement
Solution
To solve for the equation of the parabola in the form that passes through the points , we need to find the coefficients , , and .
We will substitute each point into the general equation and solve the resulting system of three equations.
Step 1: Set up the system of equations
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For the point :
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For the point :
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For the point :
Step 2: Solve the system of equations
Now we have the following system of linear equations:
1. & \quad 9a - 3b + c = 43 \\ 2. & \quad 25a + 5b + c = 27 \\ 3. & \quad 16a - 4b + c = 63 \\ \end{aligned}$$ Let me solve this system to find $$a$$, $$b$$, and $$c$$.The solution to the system of equations is: $$a = 2, \quad b = -6, \quad c = 7$$ Thus, the equation of the parabola that passes through the points $$(-3, 43)$$, $$(5, 27)$$, and $$(-4, 63)$$ is: $$y = 2x^2 - 6x + 7$$ Would you like more details on how this was solved or any further questions? ### Related Questions: 1. How can we verify that this parabola passes through the given points? 2. What is the vertex of the parabola $$y = 2x^2 - 6x + 7$$? 3.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Systems of Equations
Formulas
y = ax^2 + bx + c
Substituting points into quadratic equations
Theorems
Solving systems of linear equations
Suitable Grade Level
Grades 9-11
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