Question

Find b and c so that y17x2 + bx + c has vertex ( - 10, – 7).=b=C =

Answer 1

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:

`\begin{gathered} V=(h,\text{ k)} \\ -10=(-b)/(2a) \\ -20a\text{ =-b} \\ -20(17)=-b \\ b=340 \end{gathered}`

2) And c, by plugging into the Vertex y-coordinate formula the values for a, and b:

`\begin{gathered} -7=-(\Delta)/(4a) \\ -7=(-(340^2-4(17)c))/(4(17)) \\ -7=(-(115600-68c))/(68) \\ -7=(-115600+68c)/(68) \\ -476=-115600+68c \\ -476+115600=68c \\ 115124=68c \\ c=(115124)/(68) \\ c=1693 \end{gathered}`

3) Finally, we can state that the equation's coefficient and the answer is

a=17

b= 340

c= 1693