Converting Between Forms of a Quadratic Equation

I. Converting Vertex to Standard form To convert from vertex to standard form you just follow the order of operations to remove the ( ) from the equation. Remember PEMDAS…. Exponents come before multiplication!!

Let’s work through an example… Convert to standard form. Step 1: Rewrite the equation as follows… Because to square something means to multiply it by itself

Now, FOIL the binomials… Then combine like terms inside the brackets…

Next step… Distribute the 2 inside the brackets… NOT to the +1 That gives us…..

Finally, combine like terms This is in standard form! Every vertex to standard form problem will follow the same pattern of steps…

Try this one…. Convert to standard form…

Answer: Rewrite FOIL Combine like terms Distribute Combine like terms

II. Standard to vertex form The goal is to rewrite as To be able to write the vertex form you need to know the…. Vertex! So find the vertex of the parabola the way you do to graph the equation: x=-b/2a then plug that value in to get the y-coordinate.

Let’s do one together… Convert to vertex form. STEP 1: Find the vertex. Now plug x=1 into the equation to find y. So the vertex is (1,5).

In vertex form the vertex is (h,k)… so if we know the vertex is (1,5) that means that h=1 and k=5. So let’s substitute those values into our vertex form… Becomes…

Now the only thing left to find is the “a” value. Good news, this is easy! What is “a” in the standard form? Remember, “a” is in front of the term. So a=2… The “a”’s are the same in both forms so the “a” for our vertex form is also 2. Then the vertex form becomes And we’re finished!

Try this one… Convert to vertex form.

Find the vertex. So the vertex is (-1,-7) which means h=-1 and k=-7.

The “a” value in standard form is 3 so the “a” in vertex form is 3 also. That means our vertex form is …. Now, rewrite with out the double sign…