How do you find the axis of symmetry for the function $$f(x) = 2x^2 + 4x + 1$$ ?

The axis of symmetry can be found using the formula $$x = -\frac{b}{2a}$$ . Here, $$a = 2$$ and $$b = 4$$ , so $$x = -\frac{4}{2(2)} = -1$$ .

What is the formula to find the zeros of a quadratic function?

The zeros can be found using the quadratic formula: $$x = \frac{-b \textpm \textsqrt{b^2 - 4ac}}{2a}$$ .

What does the discriminant of a quadratic function tell us?

The discriminant, given by $$D = b^2 - 4ac$$ , indicates the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D

What is the vertex form of a quadratic function?

The vertex form of a quadratic function is $$f(x) = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

How can you determine if a parabola opens upwards or downwards?

A parabola opens upwards if $$a > 0$$ and downwards if $$a

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

The coefficient 'a' determines the direction of the parabola (upward or downward) and affects the width of the parabola: larger |a| values make the parabola narrower.

What is the y-intercept of a quadratic function?

The y-intercept of a quadratic function is the point where the graph intersects the y-axis, found by evaluating $$f(0)$$ .

What is the relationship between the vertex and the axis of symmetry?

The vertex lies on the axis of symmetry, which is the line that divides the parabola into two equal halves.

How do you graph a quadratic function?

To graph a quadratic function, find the vertex, axis of symmetry, y-intercept, and zeros, then plot these points and draw a smooth curve through them.

Properties of Quadratic Functions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic function?

Back

2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic function?

Back

3.

FLASHCARD QUESTION

Front

What is the vertex of a parabola?

Back

4.

FLASHCARD QUESTION

Front

What does the axis of symmetry represent in a quadratic function?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the general shape of a quadratic function's graph?

Back

The graph of a quadratic function is a U-shaped curve called a parabola.

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