Geometry | Unit 6 | Lesson 8: Equations and Graphs | Practice Problems

Classify the graph of the equation \(x^2+y^2-8x+4y=29\).

• circle

• exponential curve

• line

• parabola

Write an equation that states \((x,y)\) is the same distance from \((4,1)\) as it is from the \(x\)-axis.

Select all equations which describe the parabola with focus \((\text- 1,\text- 7)\) and directrix \(y=3\).

• \((x-1)^2+(y-7)^2=(y+3)^2\)

• \((x+1)^2+(y+7)^2=(y-3)^2\)

• \(y=\text{-}20(x+1)^2-2\)

• \(y=\text{-}20(x+1)^2+2\)

• \(y=\text{-}\frac{1}{20}(x+1)^2-2\)

Parabola A and parabola B both have the \(x\)-axis as the directrix. Parabola A has its focus at \((3,2)\) and parabola B has its focus at \((5,4)\). Select all true statements.

• Parabola A is wider than parabola B.

• Parabola B is wider than parabola A.

• The parabolas have the same line of symmetry.

• The line of symmetry of parabola A is to the right of that of parabola B.

• The line of symmetry of parabola B is to the right of that of parabola A.

A parabola has focus \((5,1)\) and directrix \(y = \text{-}3\). Where is the parabola’s vertex?

Select the value needed in the box in order for the expression to be a perfect square trinomial. \(x^2+7x+\boxed{\phantom{3}}\)

• 3.5

• 7

• 12.25

• 14.5

Rewrite each expression as the product of 2 factors: \(x^2+3x\), \(x^2-6x-7\), \(x^2+4x+4\)

Suppose this two-dimensional figure is rotated 360 degrees using the vertical axis shown. Each small square on the grid represents 1 square inch. What is the volume of the three-dimensional figure?