Sophia: Be the Professor

Hello Class! Today we will be learning about Quadratic Functions.

The definition of a Quadratic Function is as follows: A function that can be described by an equation of the form f(x) = ax² + bx + c, where a ≠ 0. This is also known as standard form.

In some situations, you will have to use algebra to rearrange the terms to get the equation into standard from in order to figure out you a, b and c values.

x2 = 3x -1

Move all terms to left hand side

x2 - 3x + 1 = 0

a=1, b=-3, c=1

The graph of a quadratic function is a curve called a parabola, or in other words a U shaped figure. Below is an example for the value y=x^2-4x-5

Once you have your equations in the standard form, you can solve for x by using the formula:

You simply plug in the values of a, b and c and solve for x. An example is: 

Solve this equation for x: x² - 4x + 4 = 0

Solution:

What are the three coefficients (a,b,c)? Remember that "a" is the coefficient in front of the x² term, b is the coefficient in front of x, and c is that constant at the end.

Therefore, for this equation, a=1, b= -4, and c= 4.

Plug those values into the quadratic formula and solve for x:

This formula can look intimidating, but one way to learn it is through song!

In some situations you can get two values for x. But that's ok, because if you look at the graph for this type of equation, it makes sense! A parabola can certainly cross the y axis twice (meaning y=0 in two places).