Characteristics of Quadratic Functions

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It is represented as a coordinate point (h, k) in the vertex form of a quadratic function: y = a(x - h)² + k.

Front

What are x-intercepts in a quadratic function?

Back

X-intercepts are the points where the graph of the quadratic function crosses the x-axis. They are the solutions to the equation when y = 0.

Front

How do you find the vertex from a graph of a quadratic function?

Back

The vertex can be identified as the point where the parabola changes direction, which is the highest or lowest point on the graph.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph crosses the y-axis, represented as (0, k) where k is the value of the function when x = 0.

Front

How many solutions can a quadratic function have?

Back

A quadratic function can have zero, one, or two solutions, depending on the number of times the graph intersects the x-axis.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is given by the equation: y = ax² + bx + c, where a, b, and c are constants.

Front

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

Back

The 'a' value 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

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a).

Front

How can you determine the number of x-intercepts from the discriminant?

Back

The discriminant (b² - 4ac) indicates the number of x-intercepts: if it's positive, there are two; if it's zero, there is one; if it's negative, there are none.

Front

What is the vertex form of a quadratic function?

Back

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