Determine the vertex of the function f(x)=2(x+1)(x+7). You must show all algebraic steps for full marks

vertex (-4,-18)

Step-by-step explanation:

f(x)=2(x+1)(x+7)

f(x)=2(x^2+8x+7)

f(x)=2x^2+16x+14

f(x)=2(x^2+8x)+14

f(x)=2(x^2+8x+4^2-4^2)+14

f(x)=2(x^2+8x+4^2)+2(-4^2)+14

f(x)=2(x^2+8x+4^2)+2(-4^2)+14

f(x)=2(x^2+8x+4^2)-18

f(x)=2(x+4)^2-18

vertex form:

f(x)=a(x-h)^2+k

h=-4

k=-18

vertex (-4,-18)

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,