How do you complete the square for the equation $$x^2 + 6x + 5 = 0$$ ?

1. Move the constant to the other side: $$x^2 + 6x = -5$$ . 2. Take half of the coefficient of x (which is 3), square it (9), and add to both sides: $$x^2 + 6x + 9 = 4$$ . 3. Factor: $$(x + 3)^2 = 4$$ . 4. Solve: $$x + 3 = \pm 2$$ , giving $$x = -1, -5$$ .

What is the first step in using the quadratic formula?

Identify the coefficients a, b, and c from the quadratic equation in the form $$ax^2 + bx + c = 0$$ .

Solve the equation $$2x^2 + 4x - 6 = 0$$ using the quadratic formula.

Using the quadratic formula: a = 2, b = 4, c = -6. The solutions are $$x = \frac{{-4 \pm \sqrt{{4^2 - 4(2)(-6)}}}}{{2(2)}} = \frac{{-4 \pm \sqrt{{16 + 48}}}}{{4}} = \frac{{-4 \pm 8}}{{4}}$$ , giving $$x = 1, -3$$ .

What is the vertex form of a quadratic equation?

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

How do you find the vertex of the parabola represented by $$y = x^2 - 4x + 3$$ ?

To find the vertex, complete the square or use the vertex formula $$h = -\frac{b}{2a}$$ . Here, $$h = -\frac{-4}{2(1)} = 2$$ . Substitute back to find k: $$k = (2)^2 - 4(2) + 3 = -1$$ . So, the vertex is (2, -1).

What is the axis of symmetry for the quadratic equation $$y = 3x^2 + 6x + 2$$ ?

The axis of symmetry is given by the formula $$x = -\frac{b}{2a}$$ . Here, $$x = -\frac{6}{2(3)} = -1$$ .

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 and a ≠ 0.

How do you determine the nature of roots using the discriminant?

Calculate the discriminant $$D = b^2 - 4ac$$ . If D > 0, there are 2 real roots; if D = 0, there is 1 real root; if D

Completing the Square & Quadratic Formula Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

2.

FLASHCARD QUESTION

Front

What does completing the square mean?

Back

3.

FLASHCARD QUESTION

Front

What is the discriminant in a quadratic equation?

Back

4.

FLASHCARD QUESTION

Front

What does a positive discriminant indicate?

Back

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

5.

FLASHCARD QUESTION

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root, also known as a repeated or double root.

6.

FLASHCARD QUESTION

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that the quadratic equation has two complex (imaginary) roots.

7.

FLASHCARD QUESTION

Front

Back

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