Key Vocabs:

General form:

Standard/Vertex form:

Parabola: The graph of every quadratic function is a curve which is called a parabola

Axis of symmetry: A straight line that divides through the parabola into two identical parts

---

For our 10th week of Pre-Calc 11, our class began to notice some clues that could lead us into guessing what our quadratic function would look like on a graph. And from that, we learned how we can convert a general form into a standard/vertex form and vice versa. It’s important to know how we can convert between these two forms because each form can give us different clues that help us determine what our graph may look.

General –> Standard

To convert general form to standard, we need to use the completing the square method just like we did in unit 3

ex1)

• Remove the 2 as a common factor from the first 2 terms
• We then add and subtract
• In the brackets, we can see there are 4 terms in step 3, from there we multiply the 4th term (-16) by the factor 2
• The first 3 terms in the brackets can be factored into
• Then we combine -32 + 24 = -8
• Therefore, our final equation is

From the standard form, we can collect information such as the vertex (-4, -8), the width of the parabola, and where the parabola moved (up, down, right, or left)

Standard –> General 

ex2)

• To convert in general form, we start by foiling the as the exponent 2 indicate the binomials are being multiplied together
• Then we combine like terms which results our final answer to

From the general form, the information we can collect is the y-intercept and if the parabola is minimum or maximum