What is the factored form of a quadratic equation?

The factored form of a quadratic equation is $$a(x - r_1)(x - r_2)$$ , where $$r_1$$ and $$r_2$$ are the roots of the equation.

How do you determine the increasing and decreasing intervals of a quadratic function?

To determine the increasing and decreasing intervals, find the vertex using $$x = -\frac{b}{2a}$$ . The function is decreasing on the interval to the left of the vertex and increasing on the interval to the right.

What is the significance of the y-intercept in a quadratic function?

The y-intercept of a quadratic function $$f(x) = ax^2 + bx + c$$ is the point where the graph intersects the y-axis, given by the value of $$c$$ .

How do you find the roots of a quadratic equation using factoring?

To find the roots using factoring, express the quadratic in the form $$a(x - r_1)(x - r_2) = 0$$ and set each factor equal to zero: $$x - r_1 = 0$$ and $$x - r_2 = 0$$ .

What is the relationship between the roots and the 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 $$\frac{c}{a}$$ .

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 can you graph a quadratic function?

To graph a quadratic function, find the vertex, axis of symmetry, y-intercept, and roots. Plot these points and draw a smooth curve through them.

Discriminant and Graphs of Quadratics Flashcards

Student preview

14 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the discriminant of a quadratic equation?

Back

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What does a positive discriminant indicate about the roots of a quadratic?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

What does a zero discriminant indicate about the roots of a quadratic?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

What does a negative discriminant indicate about the roots of a quadratic?

Back

A negative discriminant indicates that the quadratic equation has no real roots, but two complex roots.

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

How do you find the vertex of a quadratic function in standard form?

Back

6.

FLASHCARD QUESTION

Front

What is the axis of symmetry for a quadratic function?

Back

7.

FLASHCARD QUESTION

Front

What is the general form of a quadratic equation?

Back

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