Reflashcard Quadratic Key Features

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, represented as (0, f(0)).

Front

What are x-intercepts in a quadratic function?

Back

X-intercepts are the points where the graph intersects the x-axis, also known as the roots or zeros of the function.

Front

How do you find the vertex of a quadratic function?

Back

The vertex can be found using the formula x = -b/(2a) for the quadratic equation in standard form ax^2 + bx + c.

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, given by the equation x = -b/(2a).

Front

What does the vertex represent in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

How do you determine the maximum height of a projectile modeled by a quadratic function?

Back

The maximum height is found by evaluating the y-value of the vertex of the quadratic function.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

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

Front

How can you find the roots of a quadratic equation?

Back

The roots can be found using factoring, completing the square, or applying the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the relationship between the vertex and the axis of symmetry?

Back

The vertex lies on the axis of symmetry, which is a vertical line that passes through the vertex.