Katy is between Houston and San Antonio. If the distance from Katy to San Antonio is 2 x x  5 miles and the distance from Katy to Houston is 4 12 x  miles. The total distance from Houston to San Antonio is 120 miles . Then How far is it between each City?

It is hard to read what you actually wrote, but i guess this is:

Distance to San Antonio = 2*5*x mi

Distance to Houston = 4*12*x mi

Distance from Houston to San Antonio = 120mi

Then we must have that:

2*5*x mi + 4*12*x mi = 120mi

(2*5 + 4*12)*x mi = 120mi

(10 + 48)*x mi = 120mi

x mi =120/58 mi = 2.06 mi

Now we can replace it in the above equations:

Distance to San Antonio = 2*5*2.06 mi = 20.6 mi

Distance to Houston = 4*12*2.06 mi =  98.88 mi

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

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step-by-step explanation:

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