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How To Write Parabola in The Vertex Form

Any parabola $y=ax^2+bx+c$ can be written in the vertex form as $y=a(x-h)^2+k$ . The coordinate $(h,k)$ is called the vertex of the parabola. One can find the vertex by using the formula $h=-\frac{b}{2a}$ and $k=-\frac{b^2-4ac}{2a}$ or one can complete the square to find the values of $h$ and $k$ .

The videos below will explain how to use both methods to find the vertex or to rewrite the parabola in the vertex form.

How To Do Mixture Problems

A typical of mixture problem goes something like this: What is the amount of $x\%$ salt water that need to be added to $a$ gallon of salt water with concentration $y\%$ to get solution of salt water with concetration $z\%$ . The videos below discuss this kind of problem using several approaches.

Area of 2D objects

Overview:

The videos discuss how to find the area of circle, rectangle, square, trapezoid and parallelogram.

Recall that if $r,b,h$ are radius, base and height the area of the objects above are

Circle: $A=\pi r^2$ .
Rectangle: $A=bh$ or if the length and width are $l$ and $w$ then $A=lw$ .
Trapezoid: if $b_1,b_2$ are two parallel sides of trapezoid, then the area is $A=\frac{1}{2}\frac{b_1+b_2}{h}$ .
Parallelogram: $A=bh$ ..