What is the vertex form of a quadratic function?

The vertex form is $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

How can 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 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 formula for finding the roots of a quadratic equation?

The roots can be found using the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

What is the y-intercept of a quadratic function?

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at $$x = 0$$ .

How do you graph a quadratic function?

To graph a quadratic function, find the vertex, axis of symmetry, y-intercept, and zeros, then plot these points and draw a smooth curve.

What is the effect of changing the value of 'a' in a quadratic function?

Changing 'a' affects the width and direction of the parabola: larger |a| makes it narrower, while smaller |a| makes it wider.

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's a minimum; if it opens downwards, it's a maximum.

Quadratics Unit Test: Algebra 1 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 vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on the direction of the parabola.

3.

FLASHCARD QUESTION

Front

How do you find the axis of symmetry for a quadratic function?

Back

4.

FLASHCARD QUESTION

Front

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

Back

The range is all values of y that are less than or equal to the y-coordinate of the vertex.

5.

FLASHCARD QUESTION

Front

What are the zeros of a quadratic function?

Back

6.

FLASHCARD QUESTION

Front

What does it mean for a quadratic function to have two real zeros?

Back

It means the graph intersects the x-axis at two distinct points, indicating two different solutions to the equation.

7.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic function?

Back

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