Algebra: Concepts and Connections Quadratics Practice Assign.

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 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 determine if a parabola opens up or down?

Back

A parabola opens up if the coefficient of x² (a) is positive and opens down if a is negative.

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 formula x = -b/(2a).

Front

What is the maximum value of a quadratic function?

Back

The maximum value occurs at the vertex if the parabola opens downwards.

Front

What is the minimum value of a quadratic function?

Back

The minimum value occurs at the vertex if the parabola opens upwards.

Front

How do you find the zeros of a quadratic function?

Back

The zeros can be found by factoring, using the quadratic formula, or by completing the square.

Front

What is the quadratic formula?

Back

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

Front

What does the discriminant tell you about a quadratic equation?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c.