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

For a quadratic equation $$ax^2 + bx + c = 0$$ , the sum of the roots is given by $$-\frac{b}{a}$$ and the product of the roots is given by $$\frac{c}{a}$$ .

How do you apply the quadratic formula to solve $$x^2 + 6x - 16 = 0$$ ?

Plugging into the quadratic formula: $$x = \frac{-6 \pm \sqrt{6^2 - 4(1)(-16)}}{2(1)}$$ results in $$x = \frac{-6 \pm \sqrt{36 + 64}}{2} = \frac{-6 \pm \sqrt{100}}{2} = \frac{-6 \pm 10}{2}$$ .

What does it mean if the discriminant is zero?

If the discriminant is zero, it means that the quadratic equation has exactly one real solution, also known as a repeated or double root.

How do you find the roots of the equation $$2x^2 + 2 = 9x$$ ?

Rearranging gives $$2x^2 - 9x + 2 = 0$$ . Using the quadratic formula, $$x = \frac{9 \pm \sqrt{(-9)^2 - 4(2)(2)}}{2(2)} = \frac{9 \pm \sqrt{81 - 16}}{4} = \frac{9 \pm \sqrt{65}}{4}$$ .

What is the solution to the equation $$y = -x^2 - 5x + 12$$ using the quadratic formula?

Rearranging gives $$-x^2 - 5x + 12 = 0$$ . Using the quadratic formula, the solutions are $$x = -6.77$$ and $$x = 1.77$$ .

What is the vertex of the parabola represented by $$y = 2x^2 + 4x + 1$$ ?

The vertex can be found using $$x = -\frac{b}{2a} = -\frac{4}{2(2)} = -1$$ . Plugging this back into the equation gives the vertex coordinates.

What is the effect of the coefficient 'a' in a quadratic function?

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

How do you interpret the solutions of a quadratic equation graphically?

The solutions of a quadratic equation correspond to the x-intercepts of the graph of the quadratic function.

Quadratic Formula Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

2.

FLASHCARD QUESTION

Front

What does the discriminant of a quadratic equation indicate?

Back

3.

FLASHCARD QUESTION

Front

How do you determine the number of solutions for a quadratic equation?

Back

4.

FLASHCARD QUESTION

Front

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

Back

5.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

6.

FLASHCARD QUESTION

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

7.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a quadratic function?

Back

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