Alg2 - Focus/Directrix and Systems

Front

What is the vertex of a quadratic function in the form y = a(x-h)² + k?

Back

The vertex is the point (h, k).

Front

How do you find the vertex of the parabola given by the equation y = ax² + bx + c?

Back

Use the formula h = -b/(2a) to find the x-coordinate, then substitute h back into the equation to find k.

Front

What is the standard form of a parabola?

Back

The standard form is y = a(x-h)² + k.

Front

What does the 'p' value represent in the context of parabolas?

Back

The 'p' value represents the distance from the vertex to the focus and from the vertex to the directrix.

Front

What is the focus of a parabola?

Back

The focus is a point located inside the parabola where all the reflected rays converge.

Front

What is the directrix of a parabola?

Back

The directrix is a line perpendicular to the axis of symmetry of the parabola, located outside of it.

Front

How do you determine the direction a parabola opens?

Back

If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that passes through the vertex, dividing the parabola into two mirror-image halves.

Front

How can you find the intersection points of two functions?

Back

Set the two equations equal to each other and solve for x.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola.