Exercise 28 Page 643

We want to solve the given system of inequalities by graphing.

{- x > y^{2} 4 x^{2} + 14 y^{2} \leq 56 (I) (II)

Let's graph each inequality one at a time.

We can write the boundary curve for Inequality (I) by replacing the greater than sign with an equals sign. Then we can isolate the

x -

variable.

- x = y^{2} \Leftrightarrow x = - y^{2}

We see that the

x -

variable is raised to the power of

1

and the

y -

variable is raised to the power of

2 .

Therefore, the equation matches the format of a horizontal parabola.

Standard Form : Equation : x = \frac{1}{4 c} (y - k)^{2} + h x = - 1 (y - 0)^{2} + 0

The vertex of this type of parabola is the ordered pair

(h, k) .

Therefore, the vertex of the given parabola is

(0, 0) .

To draw its graph, we need to calculate the focus and the directrix. To do so, we need to find the value of

c .

\frac{1}{4 c} = - 1

▼

Solve for

c

$LHS \cdot 4 c = RHS \cdot 4 c$

1 = - 4 c

$LHS / (- 4) = RHS / (- 4)$

\frac{1}{- 4} = c

Put minus sign in front of fraction

- \frac{1}{4} = c

Rearrange equation

c = - \frac{1}{4}