How do you find the y-intercept of the function $$y = 4x^2 - 8x + 4$$ ?

Substituting $$x = 0$$ gives $$y = 4(0)^2 - 8(0) + 4 = 4$$ , so the y-intercept is $$(0, 4)$$ .

What are the x-intercepts of a quadratic function?

The x-intercepts are the points where the graph intersects the x-axis, found by solving the equation $$ax^2 + bx + c = 0$$ .

What is the difference between a minimum and maximum value in a quadratic function?

A minimum value occurs at the vertex of a parabola that opens upwards, while a maximum value occurs at the vertex of a parabola that opens downwards.

How can you determine if a quadratic function has a minimum or maximum value?

If the coefficient $$a$$ in the standard form $$y = ax^2 + bx + c$$ is positive, the function has a minimum; if negative, it has a maximum.

What is the formula for the vertex of a parabola given in vertex form?

In vertex form $$y = a(x - h)^2 + k$$ , the vertex is given by the point $$(h, k)$$ .

What does it mean for a parabola to open upwards or downwards?

A parabola opens upwards if the coefficient $$a$$ is positive, and it opens downwards if $$a$$ is negative.

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

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

How do you find the axis of symmetry for the function $$y = 2x^2 - 4x + 1$$ ?

Using the formula $$x = -\frac{b}{2a}$$ , where $$a = 2$$ and $$b = -4$$ , the axis of symmetry is $$x = 1$$ .

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

The graph of a quadratic function is a parabola, which can open upwards or downwards.

8.1: Key Features 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

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 vertex of a quadratic function in standard form?

Back

5.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a quadratic function?

Back

6.

FLASHCARD QUESTION

Front

What is the y-intercept of a quadratic function?

Back

7.

FLASHCARD QUESTION

Front

Back

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