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

The axis of symmetry for a quadratic function in standard form $$ax^2 + bx + c$$ is given by the formula $$x = -\frac{b}{2a}$$ .

What is the process of solving a quadratic equation by completing the square?

1. Move the constant term to the other side. 2. Divide by the coefficient of $$x^2$$ if necessary. 3. Add the square of half the coefficient of $$x$$ to both sides. 4. Factor the left side and solve for $$x$$ .

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 $$\frac{c}{a}$$ .

Solve the equation by completing the square: $$n^2 + 8n = 2$$

Rearranging gives $$n^2 + 8n - 2 = 0$$ . Completing the square leads to $$n = -4 \pm \sqrt{18}$$ .

Solve the equation by completing the square: $$x^2 + 16x = 1$$

Rearranging gives $$x^2 + 16x - 1 = 0$$ . Completing the square leads to $$x = -8 \pm \sqrt{65}$$ .

Solve the equation by completing the square: $$x^2 + 8x = -1$$

Rearranging gives $$x^2 + 8x + 1 = 0$$ . Completing the square leads to $$x = -4 \pm \sqrt{15}$$ .

Solve the equation by completing the square: $$y^2 + 20y + 5 = 0$$

Rearranging gives $$y^2 + 20y + 5 = 0$$ . Completing the square leads to $$y = -10 \pm \sqrt{95}$$ .

Solve the equation by completing the square: $$v^2 + 6v + 6 = 0$$

Rearranging gives $$v^2 + 6v + 6 = 0$$ . Completing the square leads to $$v = -3 \pm \sqrt{3}$$ .

Solving Quadratic Equations by Completing the Square Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What does it mean to complete the square?

Back

3.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

4.

FLASHCARD QUESTION

Front

What is the vertex form of a quadratic equation?

Back

5.

FLASHCARD QUESTION

Front

How do you derive the quadratic formula?

Back

6.

FLASHCARD QUESTION

Front

What is the discriminant in a quadratic equation?

Back

7.

FLASHCARD QUESTION

Front

What is the significance of the vertex in a quadratic function?

Back

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

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