Solve this quadratic equation using the quadratic formula. 5 - 10x - 3x2 = 0

x = (-5 ± 2√10) / 3

Step-by-step explanation:

5 − 10x − 3x² = 0

Write in standard form:

-3x² − 10x + 5 = 0

Solve with quadratic formula:

x = [ -b ± √(b² − 4ac) ] / 2a

x = [ -(-10) ± √((-10)² − 4(-3)(5)) ] / 2(-3)

x = [ 10 ± √(100 + 60) ] / -6

x = (10 ± 4√10) / -6

x = (-5 ± 2√10) / 3

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

answer: an 8-foot rope is tied from the top of a pole to a

stake in the ground, as shown in the diagram

below

step-by-step explanation: