Parabolas in Vertex Form

Front

What is a parabola?

Back

A parabola is a symmetrical, U-shaped curve that is defined as the set of all points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point on the parabola, depending on its orientation. It is the point where the parabola changes direction.

Front

What is the vertex form of a parabola's equation?

Back

The vertex form of a parabola's equation is y = a(x - h)² + k, where (h, k) is the vertex and 'a' determines the direction and width of the parabola.

Front

How do you determine if a parabola opens up or down?

Back

If 'a' in the vertex form y = a(x - h)² + k is positive, the parabola opens up. If 'a' is negative, the parabola opens down.

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 = h, where (h, k) is the vertex.

Front

What does it mean if the vertex is a minimum point?

Back

If the vertex is a minimum point, the parabola opens upwards, and the vertex represents the lowest value of the function.

Front

What does it mean if the vertex is a maximum point?

Back

If the vertex is a maximum point, the parabola opens downwards, and the vertex represents the highest value of the function.

Front

How can you find the y-intercept of a parabola in vertex form?

Back

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

Front

What is the significance of the 'a' value in the vertex form?

Back

The 'a' value affects the width and direction of the parabola. A larger absolute value of 'a' makes the parabola narrower, while a smaller absolute value makes it wider.

Front

How do you convert from vertex form to standard form?

Back

To convert from vertex form y = a(x - h)² + k to standard form y = ax² + bx + c, expand the equation and simplify.