How do you complete the square for the equation $$x^2 + bx = c$$ ?

1. Move $$c$$ to the other side: $$x^2 + bx = c$$ . 2. Take half of $$b$$ , square it, and add to both sides: $$x^2 + bx + (b/2)^2 = c + (b/2)^2$$ . 3. Factor the left side.

What is the discriminant of a quadratic equation?

The discriminant is given by $$D = b^2 - 4ac$$ and determines the nature of the roots of the quadratic equation.

How do you find the axis of symmetry for a quadratic equation?

The axis of symmetry can be found using the formula $$x = -\frac{b}{2a}$$ .

What is a perfect square trinomial?

A perfect square trinomial is an expression of the form $$a^2 + 2ab + b^2$$ , which factors to $$(a + b)^2$$ .

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 significance of the vertex in a quadratic function?

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Completing the Square Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is 'completing the square'?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form of a perfect square trinomial.

2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What is the vertex form of a quadratic equation?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What does it mean if a quadratic equation has complex solutions?

Back

Complex solutions occur when the discriminant (b^2 - 4ac) is negative, indicating that the parabola does not intersect the x-axis.

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