Find the equation y = ax2 + bx + c of the parabola that passes through the points. To verify your result, use a graphing utility to plot the points and graph the parabola.

Question

Find the equation y = ax² + bx + c  of the parabola that passes through the points. To verify your result, use a graphing utility to plot the points and graph the parabola.

(1, 4), (2, 2), (3, −6)

Answer 1

(1,4), (2,2), (3,-6)

have a parabola through them y=-3x^2 +7x

4 =a +b + c

2 =4a+2b +c

-6 =9a+3b+c

3 equations 3 unknowns

solve by elimination and substitution or by matrix algebra

a=-3, b=7, c=0

it's a downward opening parabola with axis of symmetry x=7/6 =-b/2a