Introduction to the Quadratic Formula

Determine the discriminant for the quadratic equation 0=-2x²+3. Based on the discriminant value, how many real number solutions does the equation have?

Discriminant = b²-4ac

• 0

• 1

• 2

• 24

What are the values of a, b, and c in the quadratic equation –2x² + 4x – 3 = 0?

• a = 2, b = 4, c = 3

• a = 2, b = 4, c = –3

• a = –2, b = 4, c = 3

• a = –2, b = 4, c = – 3

Which is the graph of a quadratic equation that has a positive discriminant?

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Which shows the correct substitution of the values a, b, and c from the equation 1 = –2x + 3x² + 1 into the quadratic formula? See image for answer options.

• A

• B

• C

• D

Determine the discriminant for the quadratic equation -3=x²+4x+1. Based on the discriminant value, how many real number solutions does the equation have?

• 0

• 1

• 2

• 12

Alessandro wrote the quadratic equation -6 = x² + 4x - 1 in standard form. What is the value of c in his new equation?

• c = -6

• c = -1

• c = 5

• c = 7

Which equation has an a-value of 1, a b-value of –3, and a c-value of –5?

• $0\ =\ -3x-5+x^2$

• $0=x-3-5x^2$

• $0=3x-5-x^2$

• $0=-3x+5-x^2$

Which best explains or justifies Step 4b?

• factoring a polynomial

• multiplication property of equality

• converting to a common denominator

• addition property of equality

What is the value of the discriminant for the quadratic equation –3 = –x² + 2x?

• -8

• 4

• 8

• 16

What is the value of the discriminant, b² − 4ac, for the quadratic equation 0 = x² − 4x + 5, and what does it mean about the number of real solutions the equation has?

• The discriminant is −4, so the equation has 2 real solutions.

• The discriminant is −4, so the equation has no real solutions.

• The discriminant is 35, so the equation has 2 real solutions.

• The discriminant is 35, so the equation has no real solutions.