What is the range of a quadratic function that opens downwards?

The range of a quadratic function that opens downwards is $$(-\infty, k]$$ , where k is the y-coordinate of the vertex.

How do you factor a quadratic expression?

To factor a quadratic expression of the form $$ax^2 + bx + c$$ , find two numbers that multiply to $$ac$$ and add to $$b$$ , then rewrite the expression.

What is the quadratic formula?

The quadratic formula is used to find the roots of a quadratic equation and is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

What does the discriminant of a quadratic equation tell us?

The discriminant, given by $$b^2 - 4ac$$ , indicates the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are no real roots.

What is the factored form of a quadratic function?

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

How do you determine the maximum height of a projectile modeled by a quadratic function?

The maximum height can be found by evaluating the quadratic function at the vertex, which gives the highest point of the projectile's path.

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

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

How can you identify the roots of a quadratic function graphically?

The roots of a quadratic function can be identified as the x-intercepts of the graph, where the function value is zero.

Practice Quadratic Functions Unit Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic function?

Back

2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola represents the highest or lowest point of the graph, depending on whether it opens upwards or downwards.

4.

FLASHCARD QUESTION

Front

How do you find the vertex of a quadratic function in standard form?

Back

5.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a quadratic function?

Back

6.

FLASHCARD QUESTION

Front

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

Back

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

7.

FLASHCARD QUESTION

Front

What is the range of a quadratic function that opens upwards?

Back

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