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

To complete the square, rearrange the equation to $$x^2 + bx + (\frac{b}{2})^2 = c + (\frac{b}{2})^2$$ , then factor the left side as $$(x + \frac{b}{2})^2 = c + (\frac{b}{2})^2$$ .

How do you solve a quadratic equation by factoring?

To solve by factoring, rewrite the equation in the form $$ax^2 + bx + c = 0$$ , factor it into the form $$(px + q)(rx + s) = 0$$ , and then set each factor to zero to find the solutions.

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

The standard form of a quadratic equation is $$y = ax^2 + bx + c$$ , where $$a$$ , $$b$$ , and $$c$$ are constants.

How do you graph a quadratic function?

To graph a quadratic function, find the vertex, axis of symmetry, and intercepts, then plot these points and draw a smooth curve through them.

What is the effect of the coefficient $$a$$ on the graph of a quadratic function?

The coefficient $$a$$ determines the direction of the parabola: if $$a > 0$$ , it opens upward; if $$a

What is the process of using the quadratic formula to solve equations?

To use the quadratic formula, identify the coefficients $$a$$ , $$b$$ , and $$c$$ from the equation $$ax^2 + bx + c = 0$$ , then substitute them into the formula $$x = \frac{{-b \\pm \\sqrt{{b^2 - 4ac}}}}{{2a}}$$ .

What does it mean for a quadratic equation to have complex roots?

A quadratic equation has complex roots when the discriminant is negative (i.e., $$b^2 - 4ac

How do you identify the maximum or minimum value of a quadratic function?

The maximum or minimum value of a quadratic function in vertex form $$y = a(x - h)^2 + k$$ is given by $$k$$ , occurring at the vertex $$(h, k)$$ .

Chapter 3: Quadratic Equations (Practice Test) Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

3.

FLASHCARD QUESTION

Front

What does the discriminant of a quadratic equation indicate?

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What is the vertex form of a quadratic equation?

Back

6.

FLASHCARD QUESTION

Front

How can you determine the axis of symmetry for a quadratic function?

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 (upward or downward).

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