Chapter 9.2, Problem 36PPE

(a)

To determine

To Find:The $y-\text{intercept}$

Explanation of Solution

Given:

The given equation of the parabola is $y=x^2+bx+c$ .

Calculation:

From the given graph it is seen that the $y-\text{intercept}$ is $2$ .

Hence, the $y-\text{intercept}$ is $2$ .

(b)

To determine

To Find: The equation of the axis of symmetry.

Explanation of Solution

Given:

The given equation of the parabola is $y=x^2+bx+c$ .

Calculation:

From the given graph it is seen that the $y-\text{intercept}$ is $2$ .

Hence, the $y-\text{intercept}$ is $2$ .

(c)

To determine

To Find: The value of $b$

Answer to Problem 36PPE

The value of $b$ is $8$ .

Explanation of Solution

Given:

The given equation of the parabola is $y=x^2+bx+c$ .

The given formula is $x=-\frac{b}{2a}$

Calculation:

Take the point $\left(-4,-2\right)$ , put the value of $x$ and $a$ in the equation $x=-\frac{b}{2a}$

  $\begin{array}{l}-4=-\frac{b}{2}\\ b=8\end{array}$

Hence, the value of $b$ is $8$ .

(d)

To determine

To Find: The equation of parabola.

Answer to Problem 36PPE

The equation is $y^2=4ax$ .

Explanation of Solution

Given:

The given equation of the parabola is $y=x^2+bx+c$ .

The given formula is $x=-\frac{b}{2a}$

Calculation:

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

(e)

To determine

To Find:A point from the equation of parabola.

Answer to Problem 36PPE

The equation is $y^2=4ax$ .

Explanation of Solution

Given:

The equation of the parabola is $y^2=4ax$ .

The value of $a=1$

Calculation:

Take the point $\left(-1,-2\right)$

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

  $\begin{array}{l}-2^2=4\times 1\times x\\ x=1\end{array}$