What is a quadratic equation?

A quadratic equation is a polynomial equation of degree 2, typically in the form $$ax^2 + bx + c = 0$$ where $$a, b, c$$ are constants and $$a \neq 0$$ .

What are the roots of a quadratic equation?

The roots of a quadratic equation are the values of $$x$$ that satisfy the equation $$ax^2 + bx + c = 0$$ .

What is the vertex of a parabola?

The vertex of a parabola represented by the quadratic equation $$y = ax^2 + bx + c$$ is the point where the parabola changes direction, given by the coordinates $$(h, k)$$ where $$h = -\frac{b}{2a}$$ and $$k = f(h)$$ .

What is the axis of symmetry for a parabola?

The axis of symmetry for a parabola represented by the quadratic equation $$y = ax^2 + bx + c$$ is the vertical line given by $$x = -\frac{b}{2a}$$ .

What is the standard form of a quadratic function?

The standard form of a quadratic function is $$f(x) = ax^2 + bx + c$$ .

What is the factored form of a quadratic function?

The factored form of a quadratic function is $$f(x) = a(x - r_1)(x - r_2)$$ where $$r_1$$ and $$r_2$$ are the roots of the equation.

How do you determine if a quadratic equation has real solutions?

To determine if a quadratic equation has real solutions, calculate the Discriminant $$b^2 - 4ac$$ . If it is greater than or equal to zero, the equation has real solutions.

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

The leading coefficient $$a$$ in a quadratic equation $$ax^2 + bx + c$$ determines the direction of the parabola: if $$a > 0$$ , the parabola opens upwards; if $$a

Quadratic Formula and the Discriminant 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?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Solve using the quadratic formula: 2x^2 + 7x - 15 = 0

Back

5.

FLASHCARD QUESTION

Front

Solve for x: 3x^2 - 6x + 6 = 0

Back

6.

FLASHCARD QUESTION

Front

What is the formula for the Discriminant?

Back

7.

FLASHCARD QUESTION

Front

Back

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