What is the first step in solving $$3x^2 + 4 = -2x$$ using the Quadratic Formula?

The first step is to add $$2x$$ to both sides to rearrange the equation to standard form.

Solve using the Quadratic Formula: $$x^2 + 4x - 40 = -8$$

The solutions are $$x = -8$$ and $$x = 4$$ .

Which of the following is the correct setup for $$2x^2 - 5x + 3 = 0$$ ?

The correct setup is $$x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(2)(3)}}{2(2)}$$ .

What is the significance of the coefficients a, b, and c in the Quadratic Formula?

In the quadratic equation $$ax^2 + bx + c = 0$$ , 'a' is the coefficient of $$x^2$$ , 'b' is the coefficient of $$x$$ , and 'c' is the constant term. They determine the shape and position of the parabola.

Solve for x: $$\frac{-6 \\pm \\sqrt{8}}{2}$$

This expression simplifies to $$-3 \\pm \\sqrt{2}$$ .

Which expression is NOT equivalent to $$\frac{-6 \\pm \\sqrt{8}}{2}$$ ?

The expression $$-3 \\pm \\sqrt{8}$$ is NOT equivalent.

What is the vertex form of a quadratic function?

The vertex form of a quadratic function is given by $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

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.

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-image halves, given by the formula $$x = -\frac{b}{2a}$$ .

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

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

Solve for x: $$x^2 + 3x - 9 = 0$$ using the Quadratic Formula.

The solution is $$x = \frac{-3 \pm 3\sqrt{5}}{2}$$ .

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 in the Quadratic Formula indicate?

Back

3.

FLASHCARD QUESTION

Front

How do you rearrange a quadratic equation to use the Quadratic Formula?

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What does it mean if the discriminant is zero?

Back

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

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