b= 340
c= 1693
1) Since we have this equation 17x²+bx +c and the Vertex is (-10,7) we can find out the coefficients "b" and "c" by equating them to the Vertex formula:
[tex]\begin{gathered} V=(h,\text{ k)} \\ -10=\frac{-b}{2a} \\ -20a\text{ =-b} \\ -20(17)=-b \\ b=340 \end{gathered}[/tex]2) And c, by plugging into the Vertex y-coordinate formula the values for a, and b:
[tex]\begin{gathered} -7=-\frac{\Delta}{4a} \\ -7=\frac{-(340^2-4(17)c)}{4(17)} \\ -7=\frac{-(115600-68c)}{68} \\ -7=\frac{-115600+68c}{68} \\ -476=-115600+68c \\ -476+115600=68c \\ 115124=68c \\ c=\frac{115124}{68} \\ c=1693 \end{gathered}[/tex]3) Finally, we can state that the equation's coefficient and the answer is
a=17
b= 340
c= 1693
