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Warm-Up: Review

Express in simplest radical form.

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1

Express in simplest radical form.

1

Express in simplest radical form.

1

Express in simplest radical form.

1

Express in simplest radical form.

1

Express in simplest radical form.

1

Before finding the discriminant, set the equation equal to 0. Keep the lead coefficient positive. Write the equation in standard form.
Which equation is equivalent to the given equation?

1

Before finding the discriminant, set the equation equal to 0. Keep the lead coefficient positive. Write the equation in standard form.
Which equation is equivalent to the given equation?

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1

After we get our equation equal to zero, identify a, b, and c. Then evaluate the discriminant.

a =

b =

c =

Discriminant = b² - 4ac

Discriminant =

1

After we get our equation equal to zero, identify a, b, and c. Then evaluate the discriminant.

a =

b =

c =

Discriminant = b² - 4ac

Discriminant =

1

Set the equation equal to zero to identify a, b, and c. Then evaluate the discriminant.

a =

b =

c =

Discriminant = b² - 4ac

Discriminant =

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The quadratic formula ALWAYS works. It will always find your solutions.

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Example:

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1

Use the quadratic formula to solve the quadratic equation.

x =

1

As you used the quadratic formula to solve:

Did you notice the discriminant (under the radical)?

What is the discriminant?

discriminant =

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1

How many real solutions should we expect from 4x² + x - 2 = 0 ?

Discriminant = 0, 1 solution

Discriminant > 0, 2 solutions

Discriminant < 0, 0 solutions

Whole Number Solutions

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Use the quadratic formula to solve the quadratic equation.

discriminant =

So, the quadratic will have solutions.

The solutions are:

x =

1

Use the quadratic formula to solve the quadratic equation.

discriminant =

So, the quadratic will have solutions.

The solutions are:

x =

Complex Number Solutions

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1

Use the quadratic formula to solve the quadratic equation.

discriminant =

So, the quadratic will have solutions.

The solutions are:

x =

1

Use the quadratic formula to solve the quadratic equation.

discriminant =

So, the quadratic will have solutions.

The solutions are:

x =

What if the radical cannot be simplified?

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1

Use the quadratic formula to solve the quadratic equation.

discriminant =

So, the quadratic will have solutions.

The solutions are:

x =

1

Use the quadratic formula to solve the quadratic equation.

discriminant =

So, the quadratic will have solutions.

The solutions are:

x =

U4D7 Discriminant and Quadratic Formula 3/19

U4D7 Discriminant and Quadratic Formula 3/19

Warm-Up: Review

Express in simplest radical form.

Express in simplest radical form.

Express in simplest radical form.

Express in simplest radical form.

Express in simplest radical form.

Before finding the discriminant, set the equation equal to 0. Keep the lead coefficient positive. Write the equation in standard form.
Which equation is equivalent to the given equation?

Before finding the discriminant, set the equation equal to 0. Keep the lead coefficient positive. Write the equation in standard form.
Which equation is equivalent to the given equation?

How many real solutions should we expect from 4x² + x - 2 = 0 ?

Whole Number Solutions

Complex Number Solutions

What if the radical cannot be simplified?

Warm-Up: Review

Express in simplest radical form.

Express in simplest radical form.

Express in simplest radical form.

Express in simplest radical form.

Express in simplest radical form.

Express in simplest radical form.
Write your answer as a + bi .

Before finding the discriminant, set the equation equal to 0. Keep the lead coefficient positive. Write the equation in standard form.
Which equation is equivalent to the given equation?

Before finding the discriminant, set the equation equal to 0. Keep the lead coefficient positive. Write the equation in standard form.
Which equation is equivalent to the given equation?

How many real solutions should we expect from 4x² + x - 2 = 0 ?

Whole Number Solutions

Complex Number Solutions

What if the radical cannot be simplified?

Express in simplest radical form.
Write your answer as a + bi .

U4D7 Discriminant and Quadratic Formula 3/19

U4D7 Discriminant and Quadratic Formula 3/19

Warm-Up: Review

Express in simplest radical form.

Express in simplest radical form.

Express in simplest radical form.

Express in simplest radical form.

Express in simplest radical form.

Before finding the discriminant, set the equation equal to 0. Keep the lead coefficient positive. Write the equation in standard form.Which equation is equivalent to the given equation?

Before finding the discriminant, set the equation equal to 0. Keep the lead coefficient positive. Write the equation in standard form.Which equation is equivalent to the given equation?

How many real solutions should we expect from 4x2 + x - 2 = 0 ?

Whole Number Solutions

Complex Number Solutions

What if the radical cannot be simplified?

Warm-Up: Review

Express in simplest radical form.

Express in simplest radical form.

Express in simplest radical form.

Express in simplest radical form.

Express in simplest radical form.

Express in simplest radical form.Write your answer as a + bi .

Before finding the discriminant, set the equation equal to 0. Keep the lead coefficient positive. Write the equation in standard form.Which equation is equivalent to the given equation?

Before finding the discriminant, set the equation equal to 0. Keep the lead coefficient positive. Write the equation in standard form.Which equation is equivalent to the given equation?

How many real solutions should we expect from 4x2 + x - 2 = 0 ?

Whole Number Solutions

Complex Number Solutions

What if the radical cannot be simplified?

Express in simplest radical form.Write your answer as a + bi .

Before finding the discriminant, set the equation equal to 0. Keep the lead coefficient positive. Write the equation in standard form.
Which equation is equivalent to the given equation?

Before finding the discriminant, set the equation equal to 0. Keep the lead coefficient positive. Write the equation in standard form.
Which equation is equivalent to the given equation?

How many real solutions should we expect from 4x² + x - 2 = 0 ?

Express in simplest radical form.
Write your answer as a + bi .

Before finding the discriminant, set the equation equal to 0. Keep the lead coefficient positive. Write the equation in standard form.
Which equation is equivalent to the given equation?

Before finding the discriminant, set the equation equal to 0. Keep the lead coefficient positive. Write the equation in standard form.
Which equation is equivalent to the given equation?

How many real solutions should we expect from 4x² + x - 2 = 0 ?

Express in simplest radical form.
Write your answer as a + bi .