What is the value of the discriminant for the equation $$2x^2 + 2x - 12 = 0$$ ?

For the equation $$2x^2 + 2x - 12 = 0$$ , the discriminant is $$D = (2)^2 - 4(2)(-12) = 4 + 96 = 100$$ .

How do you find the roots of the equation $$x^2 + 4x - 40 = -8$$ using the quadratic formula?

First, rewrite the equation as $$x^2 + 4x + 32 = 0$$ . Then apply the quadratic formula: $$x = \frac{-4 \pm \sqrt{(4)^2 - 4(1)(32)}}{2(1)}$$ .

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

The first step is to ensure the equation is in the standard form $$ax^2 + bx + c = 0$$ .

What are the coefficients in the quadratic equation $$3x^2 + 6x + 2 = 0$$ ?

The coefficients are: a = 3, b = 6, c = 2.

What is the formula for the vertex of a parabola represented by a quadratic equation?

The vertex of the parabola given by the equation $$y = ax^2 + bx + c$$ is located at $$x = -\frac{b}{2a}$$ .

How can you check if your solutions to a quadratic equation are correct?

You can check your solutions by substituting them back into the original equation to see if they satisfy it.

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

The sum of the roots is given by $$-\frac{b}{a}$$ and the product of the roots is given by $$\frac{c}{a}$$ .

What is the standard form of a quadratic equation?

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

What does the term 'parabola' refer to in relation to quadratic equations?

A parabola is the graph of a quadratic function, which is U-shaped and can open upwards or downwards depending on the sign of the coefficient a.

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

To derive the quadratic formula, complete the square on the standard form $$ax^2 + bx + c = 0$$ and solve for x.

Quadratic Formula Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

2.

FLASHCARD QUESTION

Front

What does the discriminant tell us about the solutions of a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What is the significance of the term 'real solutions' in the context of quadratic equations?

Back

Real solutions refer to the values of x that satisfy the quadratic equation and are real numbers, as opposed to complex or imaginary numbers.

6.

FLASHCARD QUESTION

Front

What does it mean if the discriminant is equal to zero?

Back

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

7.

FLASHCARD QUESTION

Front

Back

Since the discriminant is zero (36 - 36 = 0), there is 1 solution for this equation.

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