Circle and Parabola Concepts

The video tutorial covers the identification and graphing of conic sections, focusing on circles and parabolas. It begins with recognizing a circle from a given equation by completing the square and converting it to standard form. The tutorial then shifts to parabolas, explaining how to identify and graph them by finding their vertex and intercepts. The video concludes with a brief overview of the properties of these conic sections.

What type of conic section is represented by the equation x² + y² - 2x + 4y = 4?

• Hyperbola

• Circle

• Parabola

• Ellipse

When completing the square for the equation x² - 2x + y² + 4y = 4, what value is added to both sides to complete the square for the x terms?

• 2

• 4

• 1

• 0

What is the center of the circle represented by the equation (x - 1)² + (y + 2)² = 9?

• (0, 0)

• (1, -2)

• (2, -1)

• (-1, 2)

What is the radius of the circle with the equation (x - 1)² + (y + 2)² = 9?

• 2

• 3

• 5

• 4

What is the standard form of a circle's equation centered at the origin?

• x² + y² = r²

• x² - y² = r²

• x² + y² = 0

• x² - y² = 0

Which conic section is represented by the equation 2x² + y + 12x + 16 = 0?

• Hyperbola

• Circle

• Ellipse

• Parabola

In the equation y = -2x² - 12x - 16, what are the x-intercepts?

• x = -2 and x = -4

• x = 1 and x = 3

• x = 2 and x = 4

• x = -1 and x = -3

What is the vertex of the parabola given by the equation y = -2(x + 3)² + 2?

• (-2, 3)

• (-3, 2)

• (3, -2)

• (2, -3)

What is the general shape of the graph of y = -2x²?

• Opens upward

• Vertical line

• Opens downward

• Horizontal line

What is the effect of the coefficient -2 in the equation y = -2x² on the parabola's graph?

• It opens upward and is wider

• It opens downward and is narrower

• It opens upward and is narrower

• It opens downward and is wider