Exercise 44 Page 348

Before we begin, note that in the given equation the variable that is raised to the second power is y. x=1/8y^2 Therefore, the axis of symmetry of the parabola is a horizontal line.

Finding the Desired Information

x=1/4 p(y- k)^2+ h We need to identify the values of h, k, and p. Let's start with p. To do so, we will solve the equation 14 p= 18. We set it equal to 18 because this is the coefficient of the y^2-term.

1/4p=1/8

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Solve for p

MultEqn

LHS * 8=RHS* 8

1/4p(8)=1

MoveRightFacToNumOne

1/b* a = a/b

8/4p=1

ReduceFrac

a/b=.a /4./.b /4.

2/p=1

MultEqn

LHS * p=RHS* p

2=p

RearrangeEqn

Rearrange equation

p=2

Knowing that p= 2, we can rewrite the equation. x=1/8y^2 ⇕ x=1/4( 2)(y- 0)^2+ 0 Now we have that h= 0, k= 0, and p= 2. By recalling the corresponding formulas, we can find the focus, directrix, and axis of symmetry of the parabola.

	Focus	Directrix	Axis of Symmetry
Formula	( h+ p, k)	x= h- p	y= k
Value	( 0+ 2, 0) ⇓ (2,0)	x= 0- 2 ⇓ x=- 2	y= 0

Drawing the Parabola

Now, let's draw the parabola using the obtained information.