Exploring the Quadratic Formula and Discriminant

This video tutorial introduces the quadratic formula, explains its importance, and teaches a song to help memorize it. The instructor provides detailed examples of solving quadratic equations using the formula and discusses the concept of the discriminant, explaining how it determines the nature of the solutions. The video emphasizes the importance of understanding and simplifying the radicals in the quadratic formula.

What is the quadratic formula used for?

• Solving quadratic equations that cannot be factored

• Solving linear equations

• Finding the area of a circle

• Calculating the slope of a line

Tags

CCSS.HSA-REI.B.4B

What is the mnemonic song for the quadratic formula?

• Row, row, row your boat, gently down the stream

• Due to a hang low under negative b plus or minus square root b squared minus 4ac

• Twinkle twinkle little star, how I wonder what you are

• Jack and Jill went up the hill to fetch a pail of water

Tags

CCSS.RI.9-10.5

CCSS.RI.8.5

CCSS.RI.8.3

CCSS.RI.11-12.3

CCSS.RI.9-10.3

In the first example, what are the values of a, b, and c?

• a = 1, b = 3, c = -7

• a = 4, b = 3, c = 2

• a = 2, b = -16, c = -27

• a = 3, b = -1, c = 8

What is the simplified form of the quadratic formula result in the first example?

• 4 ± 2√10

• 1 ± √37

• 16 ± √40

• 4 ± √10

Tags

CCSS.HSA-REI.B.4B

In the second example, what is the value of b?

• -7

• 4

• 3

• 1

Tags

CCSS.8.EE.C.7B

What is the final answer for the second example?

• 3 ± √28

• 1 ± √37

• 16 ± √40

• 4 ± √10

Tags

CCSS.HSA-REI.B.4B

In the third example, what is the value of the discriminant?

• 37

• -95

• -23

• 40

Tags

CCSS.HSA-REI.B.4B

What is the square root of a negative number represented by?

• j

• i

• l

• k

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CCSS.HSN.CN.A.1

What does the discriminant tell us about the solutions of a quadratic equation?

• The vertex of the quadratic equation

• The slope of the quadratic equation

• The y-intercept of the quadratic equation

• The number of real and imaginary solutions

Tags

CCSS.HSA-REI.B.4B

If the discriminant is greater than zero, how many real solutions are there?

• One

• None

• Two

• Three

Tags

CCSS.HSA-REI.B.4B