Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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.

Front

What is the vertex of a parabola?

Back

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

Front

How do you find the vertex of a parabola given by the equation y = ax^2 + bx + c?

Back

The x-coordinate of the vertex can be found using the formula x = -b / (2a).

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts, also known as zeros, are the points where the graph of the function crosses the x-axis, found by solving the equation f(x) = 0.

Front

What is the axis of symmetry in a parabola?

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 it mean for a parabola to open upwards?

Back

A parabola opens upwards if the coefficient 'a' in the quadratic function f(x) = ax^2 + bx + c is positive.

Front

What does it mean for a parabola to open downwards?

Back

A parabola opens downwards if the coefficient 'a' in the quadratic function f(x) = ax^2 + bx + c is negative.

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, express it in the form (x - p)(x - q) = 0, where p and q are the roots, then set each factor to zero.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).