Quadratic formula and discriminant
Flashcard
•
Mathematics
•
8th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the quadratic formula?
Back
The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.
Tags
CCSS.HSA-REI.B.4B
2.
FLASHCARD QUESTION
Front
What does the discriminant tell us?
Back
The discriminant (D = b² - 4ac) indicates the nature of the roots of a quadratic equation: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.
Tags
CCSS.HSA-REI.B.4B
3.
FLASHCARD QUESTION
Front
How do you calculate the discriminant for the equation x² + 7x + 13?
Back
For the equation x² + 7x + 13, the discriminant is D = 7² - 4(1)(13) = 49 - 52 = -3.
Tags
CCSS.HSA-REI.B.4B
4.
FLASHCARD QUESTION
Front
What is the significance of a negative discriminant?
Back
A negative discriminant indicates that the quadratic equation has no real solutions, meaning the graph does not intersect the x-axis.
Tags
CCSS.HSA-REI.B.4B
5.
FLASHCARD QUESTION
Front
Solve for x: x² - 3x = 5.
Back
Rearranging gives x² - 3x - 5 = 0. Using the quadratic formula, x = (3 ± √(9 + 20)) / 2 = (3 ± √29) / 2.
Tags
CCSS.HSA-REI.B.4B
6.
FLASHCARD QUESTION
Front
What are the roots of the equation 3x² = 16x + 12?
Back
Rearranging gives 3x² - 16x - 12 = 0. Using the quadratic formula, the roots are x = -0.67 and x = 6.
Tags
CCSS.HSA-REI.B.4B
7.
FLASHCARD QUESTION
Front
If the discriminant is -2, how many real solutions are there?
Back
There are no real solutions because the discriminant is negative.
Tags
CCSS.HSA-REI.B.4B
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