How do you complete the square for the equation $$x^2 - 8x - 2 = 0$$ ?

1. Move the constant to the other side: $$x^2 - 8x = 2$$ . 2. Take half of the coefficient of x, square it: $$(-4)^2 = 16$$ . 3. Add 16 to both sides: $$x^2 - 8x + 16 = 18$$ . 4. Factor: $$(x - 4)^2 = 18$$ . 5. Solve: $$x = 4 \pm 3\text{√}2$$ .

How do you solve the equation $$9x + 17 + 10x^2 = 9x^2 + 16 + 6x$$ by completing the square?

1. Rearrange to standard form: $$x^2 + 3x + 1 = 0$$ . 2. Move the constant: $$x^2 + 3x = -1$$ . 3. Complete the square: $$(x + 1.5)^2 = 3.25$$ . 4. Solve: $$x = -1.5 \\pm \text{√}3.25$$ .

How do you complete the square for the equation $$-5x - 10 = -x^2$$ ?

1. Rearrange: $$x^2 - 5x - 10 = 0$$ . 2. Move the constant: $$x^2 - 5x = 10$$ . 3. Complete the square: $$(x - 2.5)^2 = 16.25$$ . 4. Solve: $$x = 2.5 \\pm \text{√}16.25$$ .

What is the formula for the roots of a quadratic equation?

The roots of a quadratic equation $$ax^2 + bx + c = 0$$ can be found using the quadratic formula: $$x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$$ .

How do you solve the equation $$5x^2 - 17x - 3 = 4x^2 - 10x - 2$$ by completing the square?

1. Rearrange: $$x^2 - 7x - 1 = 0$$ . 2. Move the constant: $$x^2 - 7x = 1$$ . 3. Complete the square: $$(x - 3.5)^2 = 13.25$$ . 4. Solve: $$x = 3.5 \\pm \text{√}13.25$$ .

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

The coefficients a, b, and c determine the shape, position, and direction of the parabola. The sign of a indicates whether it opens upwards (a > 0) or downwards (a

What is the axis of symmetry in a quadratic function?

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

How do you derive the vertex from the standard form of a quadratic equation?

To find the vertex from the standard form $$y = ax^2 + bx + c$$ , use the formulas: $$h = -\frac{b}{2a}$$ and $$k = f(h)$$ , where f(h) is the value of the function at x = h.

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

The vertex represents the maximum or minimum point of the parabola, indicating the highest or lowest value of the function.

How can completing the square help in graphing a quadratic function?

Completing the square allows you to rewrite the quadratic in vertex form, making it easier to identify the vertex and the direction of the parabola.

What is the effect of changing the value of 'a' in a quadratic equation?

Changing the value of 'a' affects the width and direction of the parabola: larger |a| makes it narrower, while smaller |a| makes it wider.

7.1 - Complete the Square Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the process of completing the square in a quadratic equation?

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2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

3.

FLASHCARD QUESTION

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4.

FLASHCARD QUESTION

Front

What is the vertex form of a quadratic function?

Back

5.

FLASHCARD QUESTION

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Back

6.

FLASHCARD QUESTION

Front

What is the significance of the discriminant in a quadratic equation?

Back

7.

FLASHCARD QUESTION

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