How do you determine the number of real roots of a quadratic equation?

The number of real roots can be determined using the discriminant, $$D = b^2 - 4ac$$ . If $$D > 0$$ , there are two distinct real roots; if $$D = 0$$ , there is one real root; if $$D

What is the standard form of a quadratic equation?

The standard form of a quadratic equation is $$y = ax^2 + bx + c$$ , where $$a$$ , $$b$$ , and $$c$$ are constants.

How can you convert from standard form to factored form?

To convert from standard form to factored form, you can factor the quadratic expression, often using methods like grouping or the quadratic formula.

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

The roots of a quadratic function are the x-values where the graph intersects the x-axis, while the vertex is the point where the graph reaches its maximum or minimum value.

What does it mean for a quadratic function to have complex roots?

A quadratic function has complex roots when the discriminant is negative, indicating that the parabola does not intersect the x-axis.

How do you graph a quadratic function in factored form?

To graph a quadratic function in factored form, identify the roots, plot the vertex, and use the direction of the parabola to sketch the graph.

What is the effect of changing the value of 'b' in a quadratic equation?

Changing the value of 'b' affects the position of the vertex and the axis of symmetry, but does not change the number of roots.

How can you verify the roots of a quadratic equation?

You can verify the roots by substituting them back into the original equation to see if they yield a true statement (i.e., equal to zero).

Quadratics: Factored Form Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the factored form of a quadratic equation?

Back

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

2.

FLASHCARD QUESTION

Front

What are the roots of a quadratic equation?

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

How do you find the sum of the roots in a quadratic equation?

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

What is the vertex of a quadratic function?

Back

5.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSF-IF.C.7A

6.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSF-IF.C.7A

7.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a quadratic function?

Back

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