4.7 - The Quadratic Formula

4.7 - The Quadratic Formula

Objective

To solve quadratic equations using the quadratic formula
To determine the number of solutions by using the discriminant

Solving quadratic equations

But...

​What if we can't square root or factor?

The quadratic formula actually will solve any quadratic equation, no matter how simple or challenging. But it is particularly useful when our equation cannot be factored or has complex number solutions.

Example

Open Ended

Your turn. Solve $$6x^2-11x-10=0$$ using the quadratic formula.

How many solutions?

When we learned to solve quadratics by factoring, we learned that quadratic equations have two solutions. It turns out that by evaluating one expression within the quadratic formula we can classify those solutions.

The Discriminant

Number of Solutions

Multiple Choice

Determine the value of the discriminant

x² + 7x + 13=0

• 101

• 3

• -101

• -3

Multiple Choice

Describe the number and type solutions for the following:

x² + 7x + 13

• 2 real solutions

• 2 non-real solutions

• 1 real solution

• 1 non-real solution

Match

Match the graph with the value of its discriminant

• $$b^2-4ac\ <0$$

• $$b^2-4ac\ =0$$

• $$b^2-4ac\ >0$$

Poll

Select the image that most closely describes how you feel about your ability to solve quadratic equations using the quadratic formula:

Keep Going:

Try at least two more items on the notes page before the end of class