Question 1

The set of all points (x, y) in a plane that are equidistant from a fixed line, the directrix, and a fixed point, the focus, not on the line.

Accepted Answer

Parabola

Answer

Circle

Answer

Hyperbola

Answer

Ellipse

Question 2

Find the standard form of the equation of the parabola with vertex at the origin and focus (2, 0)

Accepted Answer

Answer

Answer

Answer

Answer

Question 3

Find the standard form of the equation of the parabola with vertex (2, 1) and focus (2, 4).

Accepted Answer

<math>\left(x-2\right)^2=12\left(y-1\right)</math>

Answer

<math>\left(x-2\right)^2=6\left(y-1\right)</math>

Answer

<math>\left(x-2\right)^2=4\left(y-1\right)</math>

Answer

<math>\left(x-2\right)^2=16\left(y-1\right)</math>

Answer

<math>\left(y-2\right)^2=3\left(x-1\right)</math>

Question 4

Find the vertex of the parabola $y=-\frac{1}{2}x^2-x+\frac{1}{2}$

Accepted Answer

(-1, 1)

Answer

<math>\left(\frac{1}{2},1\right)</math>

Answer

<math>\left(\frac{1}{2},-2\right)</math>

Answer

<math>\left(1,-1\right)</math>

Answer

(1, 2)

Answer

<math>\left(-\frac{1}{2},1\right)</math>

Question 5

Write an equation of the parabola with vertical axis of symmetry, vertex at the point (2, 3), and passing through the point (4, 5).

Accepted Answer

<math>\left(x-2\right)^2=2\left(y-3\right)</math>

Answer

<math>\left(y-3\right)^2=4\left(x-2\right)</math>

Answer

<math>\left(y-3\right)^2=2\left(x-2\right)</math>

Answer

<math>\left(x-2\right)^2=4\left(y-3\right)</math>

Answer

<math>\left(y-3\right)^2=\frac{1}{2}\left(x-2\right)</math>

Question 6

Give the equation of the latus rectum of the parabola $y=-\frac{1}{2}x^2-x+\frac{1}{2}$

Accepted Answer

Answer

Answer

Answer

Answer

Question 7

Convert the equation of a parabola $y=-\frac{1}{2}x^2-x+\frac{1}{2}$ to vertex form.

Accepted Answer

<math>y=\left(x-12\right)^2+13</math>

Answer

<math>y=\left(x+12\right)^2+13</math>

Answer

<math>y=\left(x-12\right)^2+301</math>

Answer

<math>y=\left(x-12\right)^2+301</math>

Answer

<math>y=\left(x-24\right)^2+13</math>

Answer

<math>y=12\left(x-24\right)^2+13</math>

Question 8

What are the x-intercepts of the parabola with a vertex form of $y=-\frac{1}{2}x^2-x+\frac{1}{2}$

Accepted Answer

<math>\left(3,0\right)\ and\ \left(-1,0\right)</math>

Answer

<math>\left(-3,0\right)\ and\ \left(-1,0\right)</math>

Answer

<math>\left(-5,0\right)\ and\ \left(-1,0\right)</math>

Answer

<math>\left(-3,0\right)\ and\ \left(1,0\right)</math>

Answer

<math>\left(3,0\right)\ and\ \left(5,0\right)</math>

Answer

<math>\left(1,0\right)\ and\ \left(-1,0\right)</math>

Question 9

Write the standard equation of a parabola with a focus at (2, 2) and a directrix at $y=-\frac{1}{2}x^2-x+\frac{1}{2}$

Accepted Answer

<math>\left(x-2\right)^2=12\left(y+1\right)</math>

Answer

<math>\left(x-2\right)^2=12\left(y+2\right)</math>

Answer

<math>\left(x-2\right)^2=12\left(y-1\right)</math>

Answer

<math>\left(x-2\right)^2=3\left(y+1\right)</math>

Answer

<math>\left(x-2\right)^2=3\left(y-1\right)</math>

Question 10

Write the standard equation of a parabola with a focus at (-3,-2) and a directrix at x = 1

Accepted Answer

<math>\left(y+2\right)^2=-8\left(x+1\right)</math>

Answer

<math>\left(y+2\right)^2=8\left(x-1\right)</math>

Answer

<math>\left(y+2\right)^2=8\left(x+1\right)</math>

Answer

<math>\left(y+2\right)^2=-4\left(x+1\right)</math>

Answer

<math>\left(y+2\right)^2=4\left(x+1\right)</math>

Question 11

Write the following standard form of the parabola $y=-\frac{1}{2}x^2-x+\frac{1}{2}$ into factored form

Accepted Answer

<math>y=6\left(x-1\right)\left(2x+5\right)</math>

Answer

<math>y=6\left(2x-1\right)\left(2x+5\right)</math>

Answer

<math>y=4\left(x-2\right)\left(2x+3\right)</math>

Answer

<math>y=4\left(2x-1\right)\left(x+5\right)</math>

Answer

<math>y=6\left(2x-1\right)\left(x+5\right)</math>

Question 12

Write the equation of a parabola $y=-\frac{1}{2}x^2-x+\frac{1}{2}$ in vertex form.

Accepted Answer

<math>\left(x+y\right)^2=2x-3y-5</math>

Answer

<math>\left(x+2xy+y\right)^2=2x-3y-5</math>

Answer

<math>\left(x+2xy+y\right)^2=2x+3y+5</math>

Answer

<math>\left(x+y\right)^2=2x+3y-5</math>

Answer

<math>\left(x-y\right)^2=2x+3y-5</math>

Answer

<math>\left(x+y\right)^2=-2x-3y-5</math>

Question 13

A cable suspended between two poles which are 200 ft apart has a sag of 50 ft. If the cable hangs in a form of a parabola, find its equation with the origin at its lowest point.

Accepted Answer

Answer

Answer

Answer

Answer

Question 14

A searchlight has a parabolic reflector that forms a “bowl,” which is 12 in. wide from rim to rim and 8 in. deep, as shown in the figure. If the filament of the light bulb is located at the focus, how far from the vertex of the reflector is it in inches?

Accepted Answer

Answer

Answer

Answer

Answer

Answer

Question 15

Water issuing from the end of a horizontal pipe 6 meters above the ground, forms a parabolic curve, the vertex being at the end of the pipe. At a point 2 meters below the line of the pipe, the flow of water has curved outward 3 meters beyond the vertical line through the end of the pipe. How far beyond this vertical line will the water strike the ground? Approximate the answer.

Accepted Answer

5.2 m

Answer

3.3 m

Answer

6.3 m

Answer

7.1 m

Answer

5.4 m

Answer

2.4 m

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