2/14 - Quadratic Formula - Day 2

Do Now

7

Solve the quadratic equations for all solutions using the
provided method.

1.

Solve y = x² - 7x -30 using the quadratic formula.

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.

8

Lesson Vocabulary

9

Parabola

Axis of
symmetry

x - intercept /
solution / root

y - intercept

Vertex
(max/min)

●Standard Form:
y = ax² + bx + c
(general form of a
quadratic function).

10

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.

11

Open Ended

What is the first step in solving the following quadratic function:

$$c^2+8c+20=4$$

12

Solve Quadratic Equations using the Quadratic Formula

12

So far you have solved quadratic equations by factoring, taking square roots, and by
completing the square. Today we will learn how to use the quadratic formula.

The real solutions of the quadratic equation ax2 + bx + c = 0 are

Note: We use this formula when a ≠ 0 and b2 – 4ac ≥ 0.

Labeling

Label the key to the following equation:

$$3x^2+6x-8=7$$

Drag labels to their correct position on the image

3

-8

3x²

6x

7

6

-15

Math Response

What is the quadratic formula with the following key:

$$a=3,\ b=-2,\ c=5$$

(Use + for this problem)

Type answer here

Correct Answer: \frac{-\left(-2\right)+\sqrt{\left(-2\right)^2-4\left(3\right)\left(5\right)}}{2\left(3\right)}

Deg^°

Rad

13

Solve Quadratic Equations using the Quadratic Formula

13

Example: Solve2x² – 5x + 3 = 0 using the Quadratic Formula.

Identify the values of a, b, and c.

a = 2

b = –5 c = 3

Set the equation equal to 0 if it is not already done. 2x²– 5x + 3 = 0

Carefully substitute the values into the quadratic formula.

14

Solve Quadratic Equations using the Quadratic Formula

Simplify.

15

Solve Quadratic Equations using the Quadratic Formula

15

Separate into two equations.

16

Tech Self check ✔

How can we self
check ✔ our answer?

Use your calculator or desmos to check your
work!

✅

17

Now you and your partner try on your whiteboard!

17

Example: Solve 3x² – 7x – 20 = 0 using the Quadratic Formula.

18

Tech Self check ✔

How can we self
check ✔ our answer?

Use your calculator or desmos to check
your work!

✅

​

19

Continue using the Quadratic Formula

19

Example: Solve c² + 8c + 20 = 4 using the Quadratic Formula.

Identify the values of a, b, and c.

a = 1

b = 8

c = 16

Set the equation equal to 0 by subtracting 4 on both sides of the equal
sign.

1c² + 8c + 16 = 0

Carefully substitute the values into the quadratic formula.

20

Solve Quadratic Equations using the Quadratic Formula

Simplify.

21

Solve Quadratic Equations using the Quadratic Formula

Separate into two equations.

Multiple Choice

Which graph represents a quadratic equation with one solution?

22

Tech Self check ✔

How can we self
check ✔ our answer?

Use your calculator or desmos to check
your work!

✅

Graph the function y = x² + 8x + 20. Double check that it
has x – intercept (–4, 0).

What do you notice about the previous equations and the

graphs?

Possible Solutions to a

Quadratic Function

We will only be looking at real solutions.

Multiple Choice

Daniel is solving the quadratic equation 2x² + 9x + 3 = –5. Which of
the following are the solutions to this equation?

• $$x=\frac{-9+\sqrt[]{17}}{4},\ x=\frac{-9-\sqrt[]{17}}{4}$$

• $$x=\frac{9+\sqrt[]{17}}{4},\ x=\frac{9-\sqrt[]{17}}{4}$$

• $$x=\frac{9+\sqrt[]{-145}}{4},\ x=\frac{9-\sqrt[]{-145}}{4}$$

• $$x=\frac{9+\sqrt[]{17}}{2},\ x=\frac{9-\sqrt[]{17}}{2}$$

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.

29

Open Ended

What does the discriminant tell you about a quadratic equation?

Use complete sentences: The discriminant of a quadratic equation tells you...