Chapter 5.2, Problem 84E

To determine

To identify the focus, directrix and axis of symmetry of the parabola and then graph the equation.

Answer to Problem 84E

The focus is $\left(1,0\right)$ , directrix is $y=-1$ and the axis of symmetry is x -axis

Explanation of Solution

Given information:

The equation of parabola is $y^2=4x$

Calculation :

Rewrite the equation in the standard form.

  $\begin{array}{l}{y}^2=4x\\ x=\frac{y^2}{4}\left[\text{divide both side by 4}\right]\\ x=\frac{1}{4}{y}^2\end{array}$

Compare the equation with standard equation of parabola $x=\frac{1}{4p}{y}^2$

Where p is $=1$ the focus is $\left(p,0\right)$ or $\left(1,0\right)$ and the directrix is $x=-p$ or $y=-1$ . Because y is squared the axis of symmetry is x -axis

To graph the equation make table of values

x	0	$\frac{1}{4}$	$1$	$\frac{9}{4}$
y	0	$\pm 1$	$\pm 2$	$\pm 3$