### Home > A2C > Chapter Ch7 > Lesson 7.1.5 > Problem 7-72

7-72.

Find the equation in *y* = *ax*^{2} + *bx* + *c* form of the parabola that passes through the points (1, 5), (3, 19), and (−2, 29). 7-72 HW eTool (Desmos). Homework Help ✎

Substitute the point (1, 5) into *y* = *ax*² + *bx* + *c* where *x* = 1 and *y* = 5.

Repeat the previous step with (3, 19) and (−2, 29) to create two more equations.

You have created a system of three equations with three variables. Solve the system of equations.

Refer to problem 6-71 for help.

*a* + *b* + *c* = 5

9*a* + 3*b* + *c* = 19

4 − 2*b* + *c* = 29

(*a*, *b*, *c*) = (3, −5, 7). Substitute for *a*, *b*, and *c* to find the equation of the parabola.

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