What are the zeros of the function $$f(x) = x^2 + 7x - 18$$ ?

The zeros are $$x = 2$$ and $$x = -9$$ .

What are the x-intercepts of the function $$f(x) = 4x^2 - x - 7$$ ?

The x-intercepts are given by $$x = \frac{1 \pm \sqrt{113}}{8}$$ .

What does the discriminant of a quadratic equation tell us?

The discriminant, given by $$D = b^2 - 4ac$$ , indicates the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D

What is the vertex of a parabola represented by the equation $$y = ax^2 + bx + c$$ ?

The vertex can be found using the formula $$x = -\frac{b}{2a}$$ . The y-coordinate can be found by substituting this x-value back into the equation.

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

To convert from standard form $$y = ax^2 + bx + c$$ to vertex form $$y = a(x-h)^2 + k$$ , complete the square.

What is the axis of symmetry for a quadratic function?

The axis of symmetry is a vertical line given by the equation $$x = -\frac{b}{2a}$$ .

What is the significance of the leading coefficient (a) in a quadratic equation?

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

How can you determine if a quadratic function has a maximum or minimum value?

If the leading coefficient (a) is positive, the function has a minimum value at the vertex. If a is negative, it has a maximum value.

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

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

Quadratic Formula Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the Quadratic Formula?

Back

2.

FLASHCARD QUESTION

Front

Identify the values of a, b, and c in the equation: 4x^2 - 8x - 3 = 0.

Back

a = 4, b = -8, c = -3.

3.

FLASHCARD QUESTION

Front

Back

The value of b is 5.

4.

FLASHCARD QUESTION

Front

How do you find the zeros of a quadratic function?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Use the quadratic formula to solve the equation: 2x^2 + 2x - 12 = 0.

Back

The solutions are x = 2 and x = -3.

7.

FLASHCARD QUESTION

Front

Back

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