2/13 - Quadratic Formula Day 1

Do Now

7

Simplify each expression.

1. (-12)² =

2. –(12)² =

3. f(– 5) = 3x² + x – 8

Evaluate the quadratic function.

LO: SWBAT solve quadratic equations with
real solutions using the quadratic formula.

DOL: Given 5 problems, students will
correctly solve quadratic equations with
real solutions using the quadratic formula
in at least 4 of 5 questions.

ALGI.8A - Solve quadratic equations having real solutions by factoring, taking square roots, completing the square,
and applying the quadratic formula.

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Lesson Vocabulary

Radical

Quadratic Formula

Discriminant

Taking the nth root is written
as, where x is the radicand
and n is the index.

Ex:

Ex:

The quadratic formula
provides the solutions (roots)
of a quadratic equation in
the form ax2 + bx + c = 0.
Ex:

The discriminant tells us
whether there are two
solutions, one solution, or no
solutions.
Ex:

Today you will solve quadratic equations …

using the quadratic formula.

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Let’s start by solving the quadratic equation x² − 64 = 0.

Solving Quadratics

You are going to solve this equation using both methods:

Factoring

Using Square Root

(x − 8)(x + 8) = 0

x − 8 = 0

x + 8 = 0

x = 8

x = − 8

x² − 64 = 0

x² = 64

x = −8 x = 8

+64 +64

+8 +8

−8 −8

x² − 64 = 0

Let’s do a
Recap!

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x² − 10x +18 = 0

Solving Quadratics

Can I solve this quadratic equation by factoring? Work it out and discuss
with your shoulder partner.

Let’s do
a Recap!

Solving using the Quadratic Formula

Whether an expression is…

Factorable

or

Not Factorable

x² − 10x +18

x² − 64

It always

works!

You can set it equal to zero and solve using the quadratic formula.

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Solving using the Quadratic Formula

Man by GraphicMama-team from Pixabay

The quadratic formula is

on your STAAR
Reference sheet.

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Possible Solutions to a

Quadratic Function

We will only be looking at real solutions.

Solve

1.Write the quadratic equation in
standard formax² + bx + c = 0.

2.Make a key.

Steps:

3.Using the key, plug the values into
the quadratic formula.

4.Simplify or enter into Desmos.

x² + 6 = 5x

using the Quadratic Formula
2 solutions

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​2 solutions

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Tech Self check ✔

You can use desmos to check your work!

x² - 5x + 6 = 0

x = 3

x = 2
✔

1.Write the quadratic equation in
standard formax² + bx + c = 0.

2.Make a key.

Steps:

3.Using the key, plug the values into
the quadratic formula.

4.Simplify.

1. Use the quadratic formula to solve the equation below.

Whiteboard Practice

Quadratic Formula

5x² + 13x +12 = 6

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1.Write the quadratic equation in
standard formax² + bx + c = 0.

2.Make a key.

Steps:

3.Using the key, plug the values into
the quadratic formula.

4.Simplify.

Solving using the Quadratic Formula

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​1 solution

Open Ended

How would 1 solution look on a graph?

Math Response

Use the quadratic formula to solve the equation below. 

$$9x^2+12x+4$$

Type answer here

Correct Answer: x=-\frac{2}{3}

Deg^°

Rad

Simplifying the answer in its simplest form using the quadratic formula.

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​

Steps:

3.

Function k is defined as k(x) =3x² + 11x + 9 = 0.
What are the solutions to k(x) = 0?

More Practice

A.

B.

C.

D.

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​Enter answer choices in Desmos to see which one matches

Multiple Choice

Shawn wrote the quadratic equation
x² + 3x –11 = 0. Solve the equation for all
solutions using the quadratic formula.

• $$x=\frac{3+\sqrt[]{53}}{2},\ x=\frac{3-\sqrt[]{53}}{2}$$

• $$x=\frac{3+\sqrt[]{35}}{2},\ x=\frac{3-\sqrt[]{35}}{2}$$

• $$x=\frac{-3+\sqrt[]{53}}{2},\ x=\frac{-3-\sqrt[]{53}}{2}$$

• $$x=\frac{-3+\sqrt[]{35}}{2},\ x=\frac{-3-\sqrt[]{35}}{2}$$

Recap

When solving a quadratic equation you can use the …

Quadratic Formula

Always
works!

-Write the equation in standard form ax² + bx + c = 0.

-Identify a , b & c.

-Use the quadratic formula to solve the equation.

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Demonstration of Learning

DOL:Given 5
problems, students
will correctly solve
quadratic equations
with real solutions
using the quadratic
formula in at least 4
of 5 questions.

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Open Ended

How is solve quadratic equations
using the quadratic formula different or the same as solving by factoring?

Use complete sentences: Solving quadratic equations using the quadratic formula is _________ as solving by factoring ...