CA2 Flashcard 12.1-12.4

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the point where the parabola changes direction. It can be found using the formula for the vertex of a quadratic equation in the form y = ax^2 + bx + c, which is given by the coordinates (h, k) where h = -b/(2a) and k is the value of the function at h.

Front

What is the center of an ellipse?

Back

The center of an ellipse is the midpoint of the line segment that connects the two foci. It can be found from the standard form of the ellipse equation, which is (x-h)²/a² + (y-k)²/b² = 1, where (h, k) is the center.

Front

How do you solve a system of equations using elimination?

Back

To solve a system of equations using elimination, you manipulate the equations to eliminate one variable, allowing you to solve for the other variable. This often involves multiplying one or both equations by a constant to align coefficients.

Front

What is the equation of a circle in standard form?

Back

The equation of a circle in standard form is (x-h)² + (y-k)² = r², where (h, k) is the center of the circle and r is the radius.

Front

What are the foci of an ellipse?

Back

The foci of an ellipse are two fixed points located along the major axis, and they are used to define the ellipse. The distance from the center to each focus is denoted as c, where c = √(a² - b²) for an ellipse in standard form.

Front

What is the difference between a parabola and an ellipse?

Back

A parabola is a conic section that opens either upwards or downwards and has a single vertex, while an ellipse is a closed curve that is symmetric about two axes and has two foci.

Front

How do you find the distance between the foci of an ellipse?

Back

The distance between the foci of an ellipse is 2c, where c is calculated using the formula c = √(a² - b²), with a being the semi-major axis and b being the semi-minor axis.

Front

What is the standard form of the equation of an ellipse?

Back

The standard form of the equation of an ellipse is (x-h)²/a² + (y-k)²/b² = 1, where (h, k) is the center, a is the semi-major axis, and b is the semi-minor axis.

Front

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

Back

The vertex of a quadratic function represents the maximum or minimum point of the parabola, indicating the highest or lowest value of the function.

Front

How do you determine the radius of a circle from its equation?

Back

To determine the radius of a circle from its equation in standard form (x-h)² + (y-k)² = r², take the square root of r².