Question

CAN SOMEONE HELP WITH THIS QUESTION?✨

Answer 1

b = 40 , c = 70

Explanation:

given a quadratic function in standard form

y = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

x = -
`(b)/(2a)`

y = 5x² + bx + c ← is in standard form

with a = 5 and b = b , then

x = -
`(b)/(10)`

equating to the given x- coordinate of the vertex , that is - 4

-
`(b)/(10)` = - 4 ( multiply both sides by - 10 )

b = 40

then

y = 5x² + 40x + c

substitute (- 4, - 10 ) into the equation and solve for c

- 10 = 5(- 4)² + 40(- 4) + c

- 10 = 5(16) - 160 + c

- 10 = 80 - 160 + c

- 10 = - 80+ c ( add 80 to both sides )

70 = c

then b = 40 and c = 70