Tim L. answered • 11/01/12

Math or Stats? I got you. Let's do this together!

There is no need to assume the expression is equal to zero.

Instead assuming the expression is equal to an unknown y will be your best analytical guide for future advanced math classes including calculus.

2x^2 - 9x + 4 is factorable to (2x-1)(x-4) as my fellow tutors have already expounded upon.

Analytically, it's an upward parabola since there is a positive x^2 included in the expression.

If the base of the parabola is above the x axis then, then y will never equal zero so bad bad bad assumption.

Calculus is your best analytical tool. When you calculate dy/dx and set the result equal to zero, you will find the x value of the base of the parabola.

dy/dx = (4x - 9) = 0, and thus the line x = 2.25 sits on the extreme base of the upward parabola.

When y = (2x-1)(x-4) and you plug in x, you'll get y = (3.5)(-1.75) = -6.125

So the base of the parabola is located at (2.25, -6.125) where the y value of the upward parabola's extreme base is below the x axis.

Only now can you conclude there **are** two points on y where the parabola touches the x-axis.

There are an infinite many points along the parabola, but x = 4 **and** x = 1/2 when y = 0 are usually of interest.

I intentionally do not say '**or**', but rather I say '**and**' because of definitive conclusion there **are** two points where the parabola touches the x-axis (also known as **when** y = 0)