#8.3 Graphing ax^2 +bx +c
Flashcard
•
Mathematics
•
8th - 11th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the general form of a quadratic function?
Back
The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.
2.
FLASHCARD QUESTION
Front
What does the coefficient 'a' determine in the quadratic function?
Back
The coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upwards (minimum); if 'a' is negative, it opens downwards (maximum).
3.
FLASHCARD QUESTION
Front
What is the vertex of a parabola?
Back
The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.
4.
FLASHCARD QUESTION
Front
How do you find the x-coordinate of the vertex in a quadratic function?
Back
The x-coordinate of the vertex can be found using the formula x = -b/(2a).
5.
FLASHCARD QUESTION
Front
What is the y-intercept of a quadratic function?
Back
The y-intercept of a quadratic function is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.
6.
FLASHCARD QUESTION
Front
How can you determine if a quadratic function has a maximum or minimum value?
Back
You can determine if a quadratic function has a maximum or minimum value by looking at the sign of the coefficient 'a': if 'a' is positive, it has a minimum; if 'a' is negative, it has a maximum.
7.
FLASHCARD QUESTION
Front
What is the significance of the discriminant in a quadratic equation?
Back
The discriminant (b^2 - 4ac) determines the nature of the roots: if it's positive, there are two real roots; if it's zero, there is one real root; if it's negative, there are no real roots.
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