Solve the quadratic equation $$x^2 + 6x - 16 = 0$$ using the quadratic formula.

Using the quadratic formula, $$x = \frac{-6 \pm \sqrt{6^2 - 4(1)(-16)}}{2(1)} = \frac{-6 \pm \sqrt{36 + 64}}{2} = \frac{-6 \pm \sqrt{100}}{2} = \frac{-6 \pm 10}{2}$$ . The solutions are $$x = 2$$ and $$x = -8$$ .

Given the expression $$\frac{-6 \pm \sqrt{8}}{2}$$ , which of the following is NOT equivalent?

The expression $$-3 \pm \sqrt{8}$$ is NOT equivalent to $$\frac{-6 \pm \sqrt{8}}{2}$$ .

Solve the equation $$2x^2 + 2 = 9x$$ using the quadratic formula.

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 $$x^2 + 4x - 40 = -8$$ ?

Rearranging gives $$x^2 + 4x + 32 = 0$$ . Using the quadratic formula, the solutions are $$x = -8$$ and $$x = 4$$ .

What does the term 'real solution' mean in the context of quadratic equations?

A real solution refers to a solution that is a real number, as opposed to a complex number. Quadratic equations can have zero, one, or two real solutions depending on the discriminant.

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 can you simplify the expression $$\frac{-6 \pm 2\sqrt{2}}{2}$$ ?

By dividing each term by 2, it simplifies to $$-3 \pm \sqrt{2}$$ .

What is the quadratic equation in standard form?

The standard form of a quadratic equation is $$ax^2 + bx + c = 0$$ , where a, b, and c are constants and a ≠ 0.

What is the role of the square root in the quadratic formula?

The square root in the quadratic formula is used to find the values of x that satisfy the equation, allowing for the calculation of both possible solutions (the plus and minus).

What is the importance of the quadratic formula in solving quadratic equations?

The quadratic formula provides a systematic method for finding the roots of any quadratic equation, regardless of whether the equation can be factored easily.

Quadratic Formula Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What does the discriminant of a quadratic equation indicate?

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

How do you determine the number of real solutions from the discriminant?

Back

If the discriminant is greater than zero (D > 0), there are two real solutions. If it is equal to zero (D = 0), there is one real solution. If it is less than zero (D < 0), there are no real solutions.

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

What is the significance of the term 'zero' in relation to the discriminant?

Back

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

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

What is the first step in solving a quadratic equation using the quadratic formula?

Back

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

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