Quadratic Functions - All Forms
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the equation for the axis of symmetry of a quadratic function?
Back
The axis of symmetry is given by the equation x = -\frac{b}{2a}, where a and b are coefficients from the standard form of the quadratic equation ax^2 + bx + c.
2.
FLASHCARD QUESTION
Front
What is the standard form of a quadratic function?
Back
The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.
3.
FLASHCARD QUESTION
Front
What is the vertex form of a quadratic function?
Back
The vertex form of a quadratic function is f(x) = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.
4.
FLASHCARD QUESTION
Front
What is the factored form of a quadratic function?
Back
The factored form of a quadratic function is f(x) = a(x - r_1)(x - r_2), where r_1 and r_2 are the roots of the quadratic.
5.
FLASHCARD QUESTION
Front
How do you find the y-intercept of a quadratic function?
Back
The y-intercept can be found by evaluating the function at x = 0, i.e., f(0) = c in the standard form.
6.
FLASHCARD QUESTION
Front
What is the significance of the coefficient 'a' in a quadratic function?
Back
The coefficient 'a' determines the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.
7.
FLASHCARD QUESTION
Front
How do you determine the vertex of a parabola in standard form?
Back
The vertex can be found using the formula ( -\frac{b}{2a}, f(-\frac{b}{2a}) ).
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