Algebra II Quadratics - Regression and Attributes

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero. They can be found using factoring, completing the square, or the quadratic formula.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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. It can be found using the formula x = -b/(2a).

Front

How do you find the vertex of a quadratic function?

Back

The vertex of a quadratic function in standard form y = ax^2 + bx + c can be found using the coordinates (h, k), where h = -b/(2a) and k = f(h).

Front

What is a line of best fit?

Back

A line of best fit is a straight line that best represents the data on a scatter plot. It is used in regression analysis to predict values.

Front

What does it mean for a quadratic function to have real roots?

Back

A quadratic function has real roots if the discriminant (b^2 - 4ac) is greater than or equal to zero.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant determines the nature of the roots of the quadratic equation: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

How do you determine the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value of a quadratic function occurs at the vertex. If a > 0, the vertex is a minimum; if a < 0, it is a maximum.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Front

What are the characteristics of a parabola that opens upwards?

Back

A parabola that opens upwards has a minimum point at its vertex, and the arms of the parabola extend upwards.