Quadratic Functions Review

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically 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 y-intercept of a quadratic function?

Back

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

Front

What is the formula for the axis of symmetry of a quadratic function?

Back

The axis of symmetry can be found using the formula x = -\frac{b}{2a}.

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (D = b^2 - 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

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex, which can be found using the vertex formula.

Front

How do you determine if a parabola opens upwards or downwards?

Back

If the coefficient 'a' in the quadratic function f(x) = ax^2 + bx + c is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the significance of the coefficients a, b, and c in a quadratic function?

Back

The coefficient 'a' determines the direction and width of the parabola, 'b' affects the position of the vertex, and 'c' represents the y-intercept.

Front

How can you find the roots of a quadratic equation?

Back

Roots can be found using factoring, completing the square, or the quadratic formula: x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.