Chapter 9.3, Problem 11OE

To determine

a)

To find: The vertex of parabola.

Answer to Problem 11OE

The vertex of the given parabola is $\left(-3,1\right)$ .

Explanation of Solution

Given information: The equation of parabola $x+3=\frac{1}{4}{\left(y-1\right)}^2$

Formula used: $x-h=a{\left(y-k\right)}^2$

Calculation: Compare $x+3=\frac{1}{4}{\left(y-1\right)}^2$ to $x-h=a{\left(y-k\right)}^2$

Hence, the vertex $\left(h,k\right)=\left(-3,1\right)$ .

Therefore, the required vertex is $\left(-3,1\right)$ .

To determine

b)

To find: The value of $\left|c\right|$ .

Answer to Problem 11OE

The value of $\left|c\right|$ is $1$ .

Explanation of Solution

Given information: The equation of parabola $x+3=\frac{1}{4}{\left(y-1\right)}^2$

Formula used: $x-h=a{\left(y-k\right)}^2$

Calculation: Compare $x+3=\frac{1}{4}{\left(y-1\right)}^2$ to $x-h=a{\left(y-k\right)}^2$

Hence,

  $\begin{array}{l}\because a=\left|\frac{1}{4}\right|\&\left|c\right|=\left|\frac{1}{4a}\right|\\ \therefore \left|c\right|=\left|\frac{1}{4\times \left(\frac{1}{4}\right)}\right|\\ =\left|\frac{1}{\frac{4}{4}}\right|\end{array}$

  $\therefore \left|c\right|=1$

Therefore, the value of $\left|c\right|$ is $1$ .

To determine

c)

To find: The direction of opening of the parabola.

Answer to Problem 11OE

The parabola opens right.

Explanation of Solution

Given information: The equation of parabola $x+3=\frac{1}{4}{\left(y-1\right)}^2$

Formula used: $x-h=a{\left(y-k\right)}^2$

Calculation: Compare $x+3=\frac{1}{4}{\left(y-1\right)}^2$ to $x-h=a{\left(y-k\right)}^2$

Hence,

  $\begin{array}{l}\therefore a=\frac{1}{4}\\ \therefore a>0\end{array}$

Therefore, the direction of opening of the parabola will be right.