Exercise 45 Page 348

Before we begin, note that in the given equation the variable that is raised to the second power is x. y=4x^2 Therefore, the axis of symmetry of the parabola is a vertical line.

Finding the Desired Information

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

1/4p=4

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Solve for p

MultEqn

LHS * 1/4=RHS* 1/4

1/4p(1/4)=1

MultFrac

Multiply fractions

1/16p=1

MultEqn

LHS * p=RHS* p

1/16=p

RearrangeEqn

Rearrange equation

p=1/16

Knowing that p= 116, we can rewrite the equation. y=4x^2 ⇕ y=1/4( 1/16)(x- 0)^2+ 0 Now we have that k= 0, h= 0, and p= 116. 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, k+ p)	y= k- p	x= h
Value	( 0, 0+ 1/16) ⇓ (0,1/16)	y= 0- 1/16 ⇓ y=- 1/16	x= 0

Drawing the Parabola

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