SOLUTION: 4. Determine the quadratic function,f(x)=ax˛+bx+c , whose vertex is (1, -2) and passes through the point (-1, -22). Please show all of your work. (Points : 5)

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 4. Determine the quadratic function,f(x)=ax˛+bx+c , whose vertex is (1, -2) and passes through the point (-1, -22). Please show all of your work. (Points : 5)      Log On


   

Question 466382: 4. Determine the quadratic function,f(x)=ax˛+bx+c , whose vertex is (1, -2) and passes through the point (-1, -22). Please show all of your work. (Points : 5)
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The function contains the point , hence:



so



which is to say:



The function also passes through , so:



or



which is to say



But since is two horizontal units to the left of the vertex, the independent variable value two horizontal units to the right of the vertex must produce the same function value by symmetry. Therefore the function must pass through , which, by the logic illustrated above leads us to the conclusion that:



Now that you have a system of three linear equations in three variables, solve the system to derive the required coefficients:







I use the MDETERM function in Excel to solve such systems, but there are lots of linear system solvers on the web. Or solve it yourself -- the coefficients are all integers.

John

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