### Home > A2C > Chapter Ch11 > Lesson 11.2.6 > Problem 11-122

11-122.

A parabola passes through the points (0, 5), (2, 1), and (6, 17). Homework Help ✎

What is its equation?

Where is its vertex?

Create a system of equations based on the general equation

*y* = *ax*^{2} + *bx* + *c*:

(5) = *a*(0)^{2} + *b*(0) + *c*

(1) = *a*(2)^{2} + *b*(2) + *c*

(17) = *a*(6)^{2} + *b*(6) + *c*

Simplify and solve.

5 = *c*

1 = 4*a* + 2*b* + *c*

17 = 36*a* + 6*b* + *c*

*y* = *x*^{2} − 4*x* + 5

Convert the equation you found in part (a) into graphing form.