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 do transformations affect the graph of a quadratic function?

Transformations such as shifts, stretches, and reflections affect the position and shape of the graph. For example, shifting right by $$h$$ units is represented by $$f(x) = a(x - h)^2 + k$$ .

What is the effect of changing the 'k' value in the vertex form?

Changing the 'k' value in the vertex form $$f(x) = a(x - h)^2 + k$$ shifts the graph vertically: increasing 'k' moves the graph up, while decreasing 'k' moves it down.

What is the maximum or minimum value of a quadratic function?

The maximum or minimum value of a quadratic function occurs at the vertex. If the parabola opens upwards, the vertex represents the minimum value; if it opens downwards, it represents the maximum value.

How can you determine the y-intercept of a quadratic function?

The y-intercept of a quadratic function can be found by evaluating the function at $$x = 0$$ , which gives $$f(0) = c$$ in the standard form $$f(x) = ax^2 + bx + c$$ .

What is the relationship between the roots and the graph of a quadratic function?

The roots of a quadratic function are the x-values where the graph intersects the x-axis. The number of real roots corresponds to the number of x-intercepts on the graph.

How do you graph a quadratic function?

To graph a quadratic function, identify the vertex, axis of symmetry, y-intercept, and any x-intercepts. Plot these points and draw a smooth curve through them to form the parabola.

Quadratic Functions and Their Properties Flashcards

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14 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 quadratic function?

Back

4.

FLASHCARD QUESTION

Front

How do you find the vertex from the standard form?

Back

5.

FLASHCARD QUESTION

Front

What does the 'a' value in a quadratic function indicate?

Back

6.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a quadratic function?

Back

7.

FLASHCARD QUESTION

Front

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

Back

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