Answers PrecalculusUnit Test

Unit Test — Unit test Answers

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Eliminate the parameter in the equations x = and y = t – 4. How can the rectangular equation be described?

cubic

linear

quartic

quadratic

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x = −4.6 and x = 4.6

x = −3.5 and x = 3.5

y = −4.6 and y = 4.6

y = −3.5 and y = 3.5

A picture frame has the shape of an ellipse defined by the equation with units in inches. A hook is placed on the back of the picture frame to hang it on the wall. The hook is located at one of the foci of the ellipse. What is the distance from the hook to the top of the picture frame?

2 in.

4 in.

6 in.

8 in.

Which image shows a plane slicing a double-napped cone to produce a hyperbola?

2 cones are stacked at their points. A horizontal plane goes through the center of a cone.

2 cones are stacked at their points. A plane goes diagonally through the center of a cone.

2 cones are stacked at their points. A plane goes diagonally along the sides of the cones.

2 cones are stacked at their points. A plane goes diagonally through both cones.

Which equation represents a parabola with its vertex at (1, –5) and its focus at (1, 0)?

= (x – 1)2

20(y + 5) = (x – 1)2

–20(y + 5) = (x – 1)2

= (x – 1)2

What is the rectangular form of the parametric equations x = 6t and y =?

y = StartFraction x squared Over 4 EndFraction

y = StartFraction x squared Over 9 EndFraction

y = StartFraction x Over 144 EndFraction

y = StartFraction x Over 9 EndFraction

Given , which point lies in the solution set?

(4, –0.5)

(3, –2.5)

(–2.5, 4)

(–4.5, –3)

Which graph represents the parametric equations x = 1 – t2 and y = 2t, where 0 ≤ t ≤ 5?

On a coordinate plane, a curve starts at (1, 0) and curves up through (0, 2) to (negative 24, 10).

On a coordinate plane, a curve starts at (1, 0) and curves down through (0, negative 2) to (negative 24, negative 10).

On a coordinate plane, a curve starts at (1, 0) and curves down through (2, negative 2) to (26, negative 10).

On a coordinate plane, a curve starts at (1, 0) and curves up through (2, 2) to (26, 10).

Review the graph.

y ≤ x2 – 8 and x > y2 + 1

y ≥ x2 – 8 and x < y2 + 1

y ≤ x2 + 1 and x > y2 – 8

y ≥ x2 + 1 and x < y2 – 8

Yeric designs a circular cushion by cutting pieces of fabric to sew together as the front and back of the cushion. He cuts each piece of fabric according to the equation x2 + y2 = 100 with units in inches. Based on this equation, what is the diameter of the cushion?

5 in.

10 in.

20 in.

100 in.

Which graph represents the solution of x2 + (y – 2)2 8x?

On a coordinate plane, a circle has center (0, 2) and radius 3. A parabola opens to the right and goes through (8, 8), has vertex (0, 0), and goes through (4, negative 6). Everything inside of the circle and inside of the parabola is shaded.

On a coordinate plane, a circle has center (2, 0) and radius 6. A parabola opens to the right and goes through (8, 8), has vertex (0, 0), and goes through (4, negative 6). Everything inside of the circle and outside of the parabola is shaded.

Option

Jason had to determine the solution set of . Examine the graph he drew.

The graph is correct.

The boundary should be a solid line.

The major axis should be horizontal.

The shaded region that represents the solution set should be inside the ellipse.

Which graph represents 9x2 – 16y2 – 54x + 64y – 127 = 0?

On a coordinate plane, an Ellipse has center (3, 2) and goes through (7, 2), (3, negative 1), (negative 1, 2), and (3, 5).

On a coordinate plane, an Ellipse has center (3, 2) and goes through (6, 2), (3, negative 2), (0, 3), and (3, 6).

Option

On a coordinate plane, one part of a conic graph goes through (negative 1, 6), has a vertex at (0, 2), and goes through (negative 1, negative 1). The second part goes through (7, 6), has a vertex at (6, 2), and goes through (7, negative 1).

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