This week in math we learned about the three different forms to a quadratic equation, all of which are equivalent. The three forms are called, Standard (Vertex) Form, General Form, and Factored Form. Why are there three different forms? Each form gives different clues and points on a graph. In standard form, P and Q are the vertex’s this gives the point where the parabola’s maximum or minimum reach. P can also be used to find the line of symmetry. In general form, c is the y-intercept; similarly, in factored form  x_1 x_2  are the x-intercepts. Overall, standard form is the best for graphing. Factored from can be converted to General form by multiplying the binomials, while general form can be converted into standard by completing the square.

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)

We can convert general into standard for example by completing the square.

(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}