How do you determine if a quadratic function opens upwards or downwards?

If the coefficient $$a$$ in the quadratic equation $$y = ax^2 + bx + c$$ is positive, the parabola opens upwards. If $$a$$ is negative, it opens downwards.

What is the formula for the quadratic formula?

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

What does the discriminant of a quadratic equation tell us?

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

How can you interpret the height of an object over time using a quadratic function?

The height of an object over time can be modeled by a quadratic function, where the graph shows the object's height at different time intervals, often forming a parabolic shape.

What is the relationship between the coefficients of a quadratic function and its graph?

The coefficients $$a$$ , $$b$$ , and $$c$$ affect the shape, position, and orientation of the parabola. For example, $$a$$ determines the width and direction of the opening.

How do you find the time an object is above a certain height using a quadratic function?

To find the time an object is above a certain height, set the quadratic function equal to that height and solve for $$t$$ .

What is the significance of the y-intercept in a quadratic function?

The y-intercept is the point where the graph intersects the y-axis, representing the value of $$y$$ when $$x = 0$$ .

How can you use a graph to determine the time an object is at or above a certain height?

By analyzing the graph, you can identify the intervals on the x-axis where the height (y-value) is at or above the specified height.

8-2 Interpreting Quadratic Functions Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a quadratic function?

Back

2.

FLASHCARD QUESTION

Front

How do you determine the vertex of a quadratic function?

Back

3.

FLASHCARD QUESTION

Front

What does the graph of a quadratic function look like?

Back

4.

FLASHCARD QUESTION

Front

What is the significance of the x-intercepts in a quadratic function?

Back

5.

FLASHCARD QUESTION

Front

How can you find 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, the vertex represents the minimum value; if it opens downwards, it represents the maximum value.

6.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic function?

Back

7.

FLASHCARD QUESTION

Front

What is the vertex form of a quadratic function?

Back

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