How do you determine if a quadratic can be factored?

A quadratic can be factored if its discriminant is a perfect square, indicating that the roots are rational numbers.

What is the standard form of a quadratic equation?

The standard form of a quadratic equation is $$ax^2 + bx + c = 0$$ , where a, b, and c are constants.

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

The leading coefficient (a) determines the direction of the parabola: if a > 0, the parabola opens upwards; if a

How do you solve a quadratic equation by factoring?

To solve by factoring, set the equation to zero, factor it into two binomials, and then set each binomial equal to zero to find the roots.

What is the relationship between the roots and coefficients of a quadratic equation?

For a quadratic equation $$ax^2 + bx + c = 0$$ , the sum of the roots is $$-\frac{b}{a}$$ and the product of the roots is $$\frac{c}{a}$$ .

A parabola is the graph of a quadratic function, characterized by its U-shape, which can open upwards or downwards depending on the leading coefficient.

How do you identify the vertex of a parabola from its equation?

The vertex of a parabola in standard form $$y = ax^2 + bx + c$$ can be found using the formula $$(h, k) = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$$ .

What is the importance of the quadratic formula?

The quadratic formula provides a reliable method for finding the roots of any quadratic equation, regardless of whether it can be factored.

6.01 Solving Quadratics Review Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

3.

FLASHCARD QUESTION

Front

What does the discriminant tell us?

Back

4.

FLASHCARD QUESTION

Front

How do you factor a quadratic equation?

Back

5.

FLASHCARD QUESTION

Front

What is completing the square?

Back

6.

FLASHCARD QUESTION

Front

What is the vertex form of a quadratic equation?

Back

7.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a quadratic function?

Back

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