PreCalc 11 Week 8

This week in Precalc 11 we learned about equivalent forms of the equation of a Quadratic Equation. The equivalent forms are General Form, Standard Form, and Factored Form

General form is $y=ax^2 + bx-c$

Standard form is $y= a(x-p)^2 -q$

Factored Form is $(x-x_1)(x-x_2)$

The reason that there are three different forms is that they give you different points on the chart, with general form c is the y-intercept. In standard form, p and q are the vertexes (p,q). In factored from $x_1 x_2$ are the x-intercepts. The standard form is the best for graphing. You can get the general form into standard form by completing the square and you can get factored form into general form by multiplying them together. This uses the same techniques that we used the last unit.

Example

$(x-x_1)(x-x_2)$ = $y=ax^2 + bx-c$

$y=ax^2 + bx-c$ then becomes

$y=a(x^2 + bx + ) -c -$

Now we half b and then square it so $( \frac{b}{2} )^2$ becomes $\frac{b}{4}$

$y=a(x^2 + bx + \frac{ b}{4} ) \frac{c}{4} - \frac{b}{4}$

$y=a(x + \frac{b}{4} )^2 - \frac{c-b}{4}$

Now we have standard from where p is $\frac{b}{4}$ and q is $\frac{c-b}{4}$

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