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 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

What is the increasing interval of a quadratic function that opens upwards?

For a quadratic function that opens upwards, the increasing interval is from the vertex to positive infinity, expressed as $$(h, \infty)$$ .

What is the decreasing interval of a quadratic function that opens upwards?

For a quadratic function that opens upwards, the decreasing interval is from negative infinity to the vertex, expressed as $$(-\infty, h)$$ .

How do you find the y-intercept of a quadratic function?

The y-intercept of a quadratic function is found by evaluating the function at x = 0, which gives $$f(0) = c$$ .

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

The coefficients a, b, and c affect the shape, position, and direction of the parabola. 'a' determines the width and direction, 'b' affects the position of the vertex, and 'c' gives the y-intercept.

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

The maximum or minimum value of a quadratic function occurs at the vertex and is equal to k in the vertex form $$f(x) = a(x - h)^2 + k$$ .

How can you graph a quadratic function?

To graph a quadratic function, identify the vertex, axis of symmetry, y-intercept, and x-intercepts, then plot these points and draw a smooth curve through them.

Key Features of Quadratic Graphs 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 function?

Back

3.

FLASHCARD QUESTION

Front

What does the vertex of a quadratic graph represent?

Back

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

4.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a quadratic graph?

Back

5.

FLASHCARD QUESTION

Front

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

Back

A quadratic function opens upwards if the coefficient 'a' is positive (a > 0) and downwards if 'a' is negative (a < 0).

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