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

To complete the square, rewrite as $$(x + 3)^2 - 4 = 0$$ , leading to $$(x + 3)^2 = 4$$ , giving roots $$x = -1, -5$$ .

What is the axis of symmetry in a quadratic function?

The axis of symmetry is a vertical line that divides the parabola into two mirror images, given by the formula $$x = -\frac{b}{2a}$$ .

How do you find the vertex of a parabola given by $$y = ax^2 + bx + c$$ ?

The vertex can be found using the formula $$(h, k) = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$$ .

What is the significance of the coefficient 'a' in a quadratic equation?

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

How do you solve the quadratic equation $$2x^2 - 8x + 6 = 0$$ ?

Using the quadratic formula, the solutions are $$x = 1, 3$$ .

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 does it mean if a quadratic equation has no real solutions?

It means the graph of the quadratic does not intersect the x-axis, which occurs when the discriminant is negative (i.e., $$D

How do you graph a quadratic function?

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

Quadratic Equations Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

What are the roots of a quadratic equation?

Back

4.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

5.

FLASHCARD QUESTION

Front

What does the discriminant of a quadratic equation indicate?

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What is the vertex form of a quadratic equation?

Back

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