Alg2 - Focus/Directrix and Translations

Front

What is the vertex of the parabola given by the equation y = a(x - h)² + k?

Back

The vertex is the point (h, k).

Front

How do you translate the graph of y = x² left by 4 units?

Back

The translated equation is y = (x + 4)².

Front

What is the focus of a parabola defined by the equation (y - k)² = 4p(x - h)?

Back

The focus is at the point (h + p, 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 the vertex to the directrix.

Front

How can you determine if a parabola opens upward or downward?

Back

If the coefficient of (x - h)² is positive, it opens upward; if negative, it opens downward.

Front

What is the directrix of a parabola defined by (y - k)² = 4p(x - h)?

Back

The directrix is the line x = h - p.

Front

What is the standard form of a quadratic function?

Back

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

Front

How do you find the axis of symmetry for a parabola?

Back

The axis of symmetry is the vertical line x = -b/(2a) for the quadratic equation y = ax² + bx + c.

Front

What is the significance of the '1/4p' value in a parabola?

Back

The '1/4p' value determines the width of the parabola and its direction of opening.

Front

What is the equation of a parabola that opens to the right?

Back

The equation is (y - k)² = 4p(x - h).