What are the coordinates of the vertex for the function $$f(x) = 2(x - 3)^2 + 4$$ ?

The coordinates of the vertex are $$(3, 4)$$ .

What is the axis of symmetry for the function $$f(x) = 2x^2 - 8x + 3$$ ?

The axis of symmetry is $$x = 2$$ .

How do you find the y-intercept of a quadratic function?

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

What is the formula for the quadratic formula?

The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ , used to find the roots of the quadratic equation $$ax^2 + bx + c = 0$$ .

What does the discriminant tell you about a quadratic equation?

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 maximum or minimum value of a quadratic function?

The maximum or minimum value occurs at the vertex, and can be found by evaluating $$f(h)$$ where $$h$$ is the x-coordinate of the vertex.

How do you convert from standard form to vertex form?

To convert from standard form to vertex form, complete the square on the quadratic expression.

What is the significance of the vertex in real-world applications?

In real-world applications, the vertex can represent maximum or minimum values, such as the highest point of a projectile or the lowest cost in a profit function.

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

The axis of symmetry is located exactly halfway between the two roots of the quadratic function.

Quadratic Functions and Their Properties Flashcard

Student preview

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 axis of symmetry for a quadratic function?

Back

5.

FLASHCARD QUESTION

Front

What is the vertex form of a quadratic function?

Back

6.

FLASHCARD QUESTION

Front

How do you determine the direction of opening for a parabola?

Back

7.

FLASHCARD QUESTION

Front

Back

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