Algebra ( Period 5)

Solving Quadratic Equations by Graphing 9-2

After putting the function in standard form ( ax² + bx + c) make the F(x) or y = 0 to find the x-intercept(s) of the parabola! We already know this!

x- intercepts = the roots = the zeros = the solutions of the quadratic.

One of three things will happen when you graph the parabola

1) it will go through the x axis twice (the vertex is below if it is a happy face or above it it’s  sad face.)  TWO REAL SOLUTIONS   TWO REAL ROOTS

2) It will have only one intercept (the VERTEX is on the x-axis) ONE REAL SOLUTION ONE REAL ROOT ( actually called a DOUBLE ROOT)

3) It will have NO x-intercepts ( the vertex is above if it is a happy face or below if it’s a sad face)  NO REAL SOLUTION   NO REAL ROOTS

If the x-intercept(s) are not an integer, we can estimate the roots OR use a calculator to find them exactly ( finding the zeros)

We sometimes just say that they are between the two integers that we find them on the graph!
We can also estimate to the tenths by making a table.

HOWEVER we will learn other methods in this chapter as we go along!