Quadratic Formula and Discriminant
Flashcard
•
Mathematics
•
9th Grade
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the Quadratic Formula?
Back
The Quadratic Formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).
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 solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.
Tags
CCSS.HSA-REI.B.4B
3.
FLASHCARD QUESTION
Front
How do you determine the number of solutions using the Discriminant?
Back
Calculate the Discriminant (D = b² - 4ac). If D > 0, there are two solutions; if D = 0, there is one solution; if D < 0, there are no solutions.
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
What does it mean if a quadratic opens upwards?
Back
A quadratic opens upwards if the coefficient of x² (a) is positive. This means the vertex is a minimum point.
Tags
CCSS.HSF-IF.C.7A
6.
FLASHCARD QUESTION
Front
What does it mean if a quadratic opens downwards?
Back
A quadratic opens downwards if the coefficient of x² (a) is negative. This means the vertex is a maximum point.
Tags
CCSS.HSF-IF.C.7A
7.
FLASHCARD QUESTION
Front
What is the vertex of a quadratic function?
Back
The vertex is the highest or lowest point of the parabola represented by the quadratic function. It can be found using the formula (-b/(2a), f(-b/(2a))).
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