What is the significance of the coefficient 'a' in a quadratic function?

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, it opens upwards; if negative, it opens downwards.

How can you find the roots of a quadratic equation?

By using the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

What is the axis of symmetry in a quadratic function?

The axis of symmetry is the vertical line that passes through the vertex, given by $$x = \frac{-b}{2a}$$ .

What is a polynomial function?

A polynomial function is a function that can be expressed in the form $$f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$$ where 'n' is a non-negative integer.

What is the leading coefficient of a polynomial?

The leading coefficient is the coefficient of the term with the highest degree.

How do you identify the degree of a polynomial?

The degree of a polynomial is the highest exponent of the variable in the polynomial.

What is the difference between a linear function and a quadratic function?

A linear function has a degree of 1 and graphs as a straight line, while a quadratic function has a degree of 2 and graphs as a parabola.

What is the role of the discriminant in a quadratic equation?

The discriminant, given by $$b^2 - 4ac$$ , determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Flashcard 3 & 4 Flashcard

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the formula to find the x-coordinate of the vertex of a quadratic function?

Back

2.

FLASHCARD QUESTION

Front

Back

The vertex is at x = 6.

3.

FLASHCARD QUESTION

Front

Back

The degree is 5.

4.

FLASHCARD QUESTION

Front

Back

The constant term is 6.

5.

FLASHCARD QUESTION

Front

What does the term 'vertex' refer to in a quadratic function?

Back

The vertex is the highest or lowest point on the graph of the quadratic function.

6.

FLASHCARD QUESTION

Front

How do you determine the maximum or minimum value of a quadratic function?

Back

7.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic function?

Back

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