What is the factored form of the trinomial $$x^2 + 4x + 4$$ ?

The factored form is $$(x + 2)^2$$ .

What are the solutions to the equation $$3x^2 - 6x + 80 = -4$$ ?

The solutions are $$x = 1 \\pm 3i\\sqrt{3}$$ .

What is the quadratic formula?

The quadratic formula is $$x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$$ .

What does the discriminant tell you about the roots of a quadratic equation?

The discriminant, $$b^2 - 4ac$$ , indicates the nature of the roots: if positive, two real roots; if zero, one real root; if negative, two complex roots.

What is the vertex form of a quadratic function?

The vertex form is $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex.

What is the axis of symmetry for a quadratic function?

The axis of symmetry is the vertical line $$x = -\frac{b}{2a}$$ .

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

The leading coefficient determines the direction of the parabola: if positive, it opens upwards; if negative, it opens downwards.

What is the process of factoring a quadratic equation?

Factoring involves rewriting the equation in the form $$(x - p)(x - q) = 0$$ , where p and q are the roots.

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

The sum of the roots is $$-\frac{b}{a}$$ and the product of the roots is $$\frac{c}{a}$$ .

What is the purpose of graphing a quadratic function?

Graphing helps visualize the function's behavior, including its vertex, axis of symmetry, and intercepts.

Algebra 2B - 4.7 E Learning Day Notes Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Back

2.

FLASHCARD QUESTION

Front

Back

The first step is to divide by 4.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

In problem number 3. of your notes what is b?

Back

b is -18.

5.

FLASHCARD QUESTION

Front

What is the result of taking the square root of both sides in the completing the square method?

Back

The result is solving for x.

6.

FLASHCARD QUESTION

Front

What is a perfect square trinomial?

Back

7.

FLASHCARD QUESTION

Front

Back

1. Divide by a. 2. Move c to the other side. 3. Take half of b, square it, and add to both sides.

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