3.5 Solving Quadratics Equations using the Quadratic Formula - C

3.5 - Solving Quadratics Using
The Quadratic Formula

Objective

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

​The Quadratic Formula

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:

Example:

Solve,  

Solve,  

Solve,  

Solve,  

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Math Response

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

For the 2 answers: write one answer besides the other, starting with the negative number.

Type answer here

Correct Answer: \frac{-2}{3}\frac{5}{2}

Deg^°

Rad

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

• $$b^2-4ac\ <0$$

• $$b^2-4ac\ =0$$

• $$b^2-4ac\ >0$$