Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + 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) = ax² + bx + c.

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.

Front

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

Back

To find the y-intercept, set x = 0 in the function and solve for y.

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 formula x = -b/(2a).

Front

What does the discriminant tell us about a quadratic equation?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means no real roots.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression, find two numbers that multiply to ac (the product of a and c) and add to b (the coefficient of x).

Front

What is the vertex form of a quadratic function?

Back

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

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, representing the value of the function when x = 0.

Front

How can you determine if a quadratic opens upwards or downwards?

Back

A quadratic opens upwards if a > 0 and downwards if a < 0 in the standard form f(x) = ax² + bx + c.