Exercise 1 Page 627

We want to write the equation of a parabola with vertex (0,0) and focus (0, 12). Because the x-coordinates of the vertex and the focus are both equal to 0, the axis of symmetry of the parabola is the vertical line x=0. This means that we have a vertical parabola. Equation:& y=1/4 c(x- h)^2+ k Vertex:& ( h, k) Focus:& ( h, k+ c) Since the vertex is ( 0, 0), we have that h= 0 and k= 0. Furthermore, we know that the y-coordinate of the focus is 12. 12 = k+ c Let's substitute 0 for k in the above equation, and solve for c.

1/2=k+c

Substitute

k= 0

1/2= 0+c

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Solve for c

IdPropAdd

Identity Property of Addition

1/2=c

RearrangeEqn

Rearrange equation

c=1/2

We can now write the equation of the parabola. y=1/4( 12)(x- 0)^2+ 0 Let's simplify the right-hand side!

y=1/4( 12)(x-0)^2+0

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Simplify right-hand side

MoveLeftFacToNumOne

a* 1/b= a/b

y=1/42(x-0)^2+0

DivByFracD

a/b/c= a * c/b

y=2/4(x-0)^2+0

ReduceFrac

a/b=.a /2./.b /2.

y=1/2(x-0)^2+0

AddSubTerms

Add and subtract terms

y=1/2x^2