Geometry and Algebra Concepts Assessment

The video tutorial covers various mathematical concepts, including classifying graphs based on equation features, writing and selecting parabola equations, comparing parabolas, calculating vertices, creating perfect square trinomials, factoring expressions, and calculating the volume of solids formed by rotating two-dimensional figures.

Which of the following equations represents a circle?

• x^2 + 2x + 1

• e^x

• x^2 + y^2 = r^2

• y = mx + b

What is the equation of a parabola with a focus at (4, 1) and a directrix of y = 0?

• y^2 = (x - 4)^2 + (y - 1)^2

• y^2 = (x - 4)^2 + (y - 1)^2

• y = (x - 4)^2 + (y - 1)^2

• y^2 = (x - 4)^2 + (y - 1)^2

Which equation describes a parabola with a focus at (-1, 7) and a directrix of y = 3?

• x + 1 = y - 3

• (x + 1)^2 = (y - 3)^2

• (x + 1)^2 = (y + 7)^2

• (x - 1)^2 = (y - 3)^2

If parabola A has a focus at (3, 2) and parabola B has a focus at (5, 4), which is wider?

• Parabola A

• Parabola B

• Both are the same width

• Cannot be determined

What is the vertex of a parabola with a focus at (5, 1) and a directrix of y = -3?

• (5, -2)

• (5, -1)

• (5, 0)

• (5, 2)

To make the expression a perfect square trinomial, what value should be added to x^2 + 7x + ___?

• 12.25

• 14.5

• 10.5

• 9.25

What is the product of the factors of the expression x^2 + 3x?

• x(x - 3)

• (x + 3)(x - 1)

• (x + 1)(x + 2)

• x(x + 3)

Which numbers multiply to -7 and add to -6?

• -6 and 1

• -7 and 1

• 7 and -1

• 6 and -1

What is the volume of a solid formed by rotating a figure with a base radius of 2 and height of 3 around the vertical axis?

• 20π cubic units

• 16π cubic units

• 12π cubic units

• 8π cubic units

What is the volume of the cone formed by rotating a figure with a base radius of 2 and height of 3?

• 8π cubic units

• 16π cubic units

• 4π cubic units

• 12π cubic units