Lesson 8
Equations and Graphs
- Let’s write an equation for a parabola.
Problem 1
Classify the graph of the equation \(x^2+y^2-8x+4y=29\).
circle
exponential curve
line
parabola
Problem 2
Write an equation that states \((x,y)\) is the same distance from \((4,1)\) as it is from the \(x\)-axis.
Problem 3
Select all equations which describe the parabola with focus \((\text- 1,\text- 7)\) and directrix \(y=3\).
\((x-1)^2+(y-7)^2=(y+3)^2\)
\((x+1)^2+(y+7)^2=(y-3)^2\)
\(y=\text{-}20(x+1)^2-2\)
\(y=\text{-}20(x+1)^2+2\)
\(y=\text{-}\frac{1}{20}(x+1)^2-2\)
\(y=\text{-}\frac{1}{20}(x+1)^2+2\)
Problem 4
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.
Problem 5
A parabola has focus \((5,1)\) and directrix \(y = \text{-}3\). Where is the parabola’s vertex?
Problem 6
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
Problem 7
Rewrite each expression as the product of 2 factors.
- \(x^2+3x\)
- \(x^2-6x-7\)
- \(x^2+4x+4\)
Problem 8
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?
