What is the significance of the discriminant in a quadratic equation?

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

A parabola is the graph of a quadratic function. It is a U-shaped curve that can open upwards or downwards.

What does it mean for a quadratic function to be in vertex form?

A quadratic function is in vertex form when it is expressed as $$f(x) = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

What is the standard form of a quadratic function?

The standard form of a quadratic function is $$f(x) = ax^2 + bx + c$$ , where a, b, and c are constants.

How can you determine if a quadratic function is increasing or decreasing?

A quadratic function is decreasing on the interval from negative infinity to the x-coordinate of the vertex and increasing from the vertex to positive infinity.

What is the maximum or minimum value of a quadratic function?

The maximum or minimum value occurs at the vertex. If the parabola opens upwards, it is a minimum; if it opens downwards, it is a maximum.

What is the vertex of the quadratic function $$f(x) = 2x^2 - 8x + 5$$ ?

The vertex can be found using the formula $$x = -\frac{b}{2a}$$ . Here, $$x = -\frac{-8}{2(2)} = 2$$ . Plugging this back into the function gives the vertex (2, -3).

What is the axis of symmetry for the quadratic function $$f(x) = -3x^2 + 6x + 1$$ ?

The axis of symmetry is given by $$x = -\frac{b}{2a} = -\frac{6}{2(-3)} = 1$$ .

Key Features of Quadratics Flashcards

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FLASHCARD QUESTION

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What is a quadratic function?

Back

2.

FLASHCARD QUESTION

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What does the 'a' value in a quadratic function determine?

Back

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

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