Semester 1 Exam - Algebra 2 (OL)

Front

What is the standard form of a parabola?

Back

The standard form of a parabola is given by the equation y = ax^2 + bx + c, where a, b, and c are constants.

Front

How do you find the vertex of a parabola in standard form?

Back

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

Front

What is the significance of the 'a' value in the parabola equation?

Back

The 'a' value determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards. A larger absolute value of 'a' results in a narrower parabola.

Front

What is the vertex form of a parabola?

Back

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

Front

How do you convert from standard form to vertex form?

Back

To convert from standard form y = ax^2 + bx + c to vertex form y = a(x - h)^2 + k, complete the square.

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

Front

What is the focus of a parabola?

Back

The focus of a parabola is a point located inside the curve, where all the points on the parabola are equidistant from the focus and the directrix.

Front

What is the directrix of a parabola?

Back

The directrix is a line that is perpendicular to the axis of symmetry and is used in conjunction with the focus to define the parabola.

Front

What transformations occur when a parabola is reflected over the x-axis?

Back

When a parabola is reflected over the x-axis, the 'a' value in the equation changes from positive to negative, resulting in the parabola opening downwards.

Front

How does vertical stretching affect a parabola?

Back

Vertical stretching occurs when the absolute value of 'a' in the parabola equation increases, making the parabola narrower.