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

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

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

The solutions are $$x = 2 \\pm 2i$$ .

What is a quadratic function?

A quadratic function is a function that can be expressed in the form $$f(x) = ax^2 + bx + c$$ , where a, b, and c are constants and @@a eq 0@@.

What is the vertex of a quadratic function?

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It can be found using the formula $$x = -\frac{b}{2a}$$ .

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. It is given by the equation $$x = -\frac{b}{2a}$$ .

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

The coefficient 'a' determines the direction of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

What are the x-intercepts of a quadratic function?

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis. They are the solutions to the equation $$ax^2 + bx + c = 0$$ .

How do you determine if a quadratic equation can be factored?

A quadratic equation can be factored if its Discriminant (D) is a perfect square, indicating that the roots are rational numbers.

What is the relationship between the roots and the coefficients 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 $$\frac{c}{a}$$ .

What is a complex root?

A complex root is a solution to a quadratic equation that has a real part and an imaginary part, typically occurring when the Discriminant is negative.

Quadratic Formula & Discriminant Review 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 tell us about a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What are the solutions of a quadratic equation also called?

Back

The solutions of a quadratic equation are also called roots, x-intercepts, or zeros.

6.

FLASHCARD QUESTION

Front

True or False: The quadratic equation can be used to solve quadratic equations that can or cannot be factored.

Back

True.

7.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

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