Sometimes when you have a quadratic equation in standard form you need to switch it to vertex form. Vertex form is helpful when you need to graph the equation.
Standard form of a Quadratic equation is written, ax^2 +bx +c = y
Vertex form is written, a(x-h)^2 +k=y
Let’s review the steps of switching from standard to vertex form with the following quadratic equation.
A quadratic is polynomial with x^2 as the highest term.
x^2 + 24x -1 = f(x)
Step 1. Group the x's together
X^2 + 24
Step 2.Create a space between the second and third term.
X^2 + 24 -1 =f(x)
Step 3.Now complete the square, by taking the b term (second term) and half it and square it.
24/2=12 and 12^2 =144
Step 4.Take the term from step 3, and write this term, and the negative value of the term in the space created in step 2.
X^2 +24x +144 -144 -1 =f(x)
Step 5.Now group the first three terms together to make our perfect square.
The perfect square is always the square root of what we just found in step 3. In this example it is square root of 144 which equals 12.
Step 6. Add the negative term from step 4 to the constant.
(x+12)^2 -145 = f(x)
Now we have our functions, so we can figure out our h and k.
h is the opposite of what we see which is -12
k is the same sign as what we see ( -145) and the h and k becomes your vertex that you can use to graph your quadratic equation.
The following video works two example problems and will help you understand how to change from the standard form to vertex form.