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Question 1209269: The parabola y = ax^2 + bx + c is graphed below. Find a+b+c. (The grid lines are one unit apart.)
The parabola passes through the points (-3,8), (2,5), and (6,18).
Answer by asinus(45)   (Show Source):
You can put this solution on YOUR website! **1. Set up the System of Equations**
Since the parabola passes through the points (-3, 8), (2, 5), and (6, 18), we can substitute these points into the equation y = ax² + bx + c to get a system of equations:
* **For point (-3, 8):** 8 = a(-3)² + b(-3) + c
=> 9a - 3b + c = 8
* **For point (2, 5):** 5 = a(2)² + b(2) + c
=> 4a + 2b + c = 5
* **For point (6, 18):** 18 = a(6)² + b(6) + c
=> 36a + 6b + c = 18
**2. Solve the System of Equations**
You can solve this system of equations using various methods, such as:
* **Substitution:** Solve one equation for one variable and substitute it into the other equations.
* **Elimination:** Eliminate one variable at a time by adding or subtracting multiples of the equations.
* **Matrix methods:** Use matrix operations (e.g., Gaussian elimination) to solve the system.
**Using a calculator or software (like Python with NumPy), you can find the values of a, b, and c:**
* a = 1/2
* b = -1/2
* c = 9
**3. Calculate a + b + c**
* a + b + c = 1/2 - 1/2 + 9 = 9
**Therefore, a + b + c = 9**
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