Find b and c so that y=-14x^2+bc+c has vertex (-9,8)

b = - 252 and c = - 1126

the equation of a parabola in vertex form is

y a (x - h) ² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

y = - 14 (x + 9) ² + 8 ← equation in vertex form

expand and compare coefficients

y = - 14 (x² + 18x + 81) + 8 = - 14x² - 252x - 1134 + 8

compare to y = - 14x² + bx + c

b = - 252 and c = - 1126