Mrs . Johnson has a total of 30 students in her class , The ratio of boys to girls is 2:3 , how many does Mrs. Johnson have in her class ?

12 boys and 18 girls

Step-by-step explanation:

If the ratio of boys to girls is 2:3, that means for every 5 students, 2 are girls and 3 are boys. That means 2/5 are girls and 3/5 are boys, so:

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