Flashcard 4.3 & 4.4

Front

What is the standard form of the equation of a parabola?

Back

The standard form of a parabola that opens upwards or downwards is given by y = a(x - h)² + k, where (h, k) is the vertex and 'a' determines the width and direction of the parabola.

Front

What is the focus of a parabola?

Back

The focus of a parabola is a fixed 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 of a parabola is a fixed line used in the definition of the parabola, such that any point on the parabola is equidistant from the focus and the directrix.

Front

How do you find the vertex of a parabola given its focus and directrix?

Back

The vertex of a parabola is located halfway between the focus and the directrix.

Front

What is the relationship between the distance from the focus to the vertex and the vertex to the directrix?

Back

The distance from the focus to the vertex is equal to the distance from the vertex to the directrix.

Front

How does the value of 'a' in the parabola equation y = a(x - h)² + k affect the graph?

Back

The value of 'a' determines the width and direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards. Larger absolute values of 'a' make the parabola narrower.

Front

What is the significance of x-intercepts in a quadratic function?

Back

The x-intercepts of a quadratic function are the points where the graph intersects the x-axis, indicating the values of x for which the function equals zero.

Front

How do you derive the equation of a quadratic function from its x-intercepts?

Back

If a quadratic function has x-intercepts at p and q, it can be expressed in factored form as y = a(x - p)(x - q), where 'a' is a constant that affects the width and direction of the parabola.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c, where 'a', 'b', and 'c' are constants.

Front

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

Back

The axis of symmetry for a parabola in standard form y = ax² + bx + c is given by the line x = -b/(2a).