Quadratics Characteristics

Front

What is the domain of a quadratic function?

Back

The set of all possible x-values for which the function is defined.

Front

What is the range of a quadratic function?

Back

The set of all possible y-values that the function can take.

Front

How do you determine the number of zeros of a quadratic function?

Back

By finding the x-intercepts of the graph, which can be determined using the quadratic formula or factoring.

Front

What is the vertex of a quadratic function?

Back

The highest or lowest point of the parabola, depending on its orientation.

Front

What is the standard form of a quadratic function?

Back

f(x) = ax² + bx + c, where a, b, and c are constants.

Front

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

Back

It determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What is the axis of symmetry in a quadratic function?

Back

A vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

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

Back

The discriminant (b² - 4ac) determines the number of real solutions: if > 0, two solutions; = 0, one solution; < 0, no real solutions.

Front

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

Back

By evaluating the function at x = 0, which gives the point (0, c) in the standard form.

Front

What is the vertex form of a quadratic function?

Back

f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.