Chapter 6.8, Problem 62STP

a.

To determine

To calculate: The discriminant of the function $y=0.00012x^2+6$ .

Answer to Problem 62STP

The value of the discriminant is $-2.88\times {10}^{-3}$ .

Explanation of Solution

Given information:

The supporting cables of the Golden Gate Bridge are shaped like parabola and modelled by equation $y=0.00012x^2+6$ where x is the distance from axis of symmetry and y is the height of cables.

Formula used:

For a quadratic equation $a{x}^2+bx+c=0$ the discriminant Dis $D=b^2-4ac$ .

Calculation:

Consider the equation $0.00012x^2+6=0$

Recall that for a quadratic equation $a{x}^2+bx+c=0$ the discriminant Dis $D=b^2-4ac$ .

Therefore, discriminant of provided equation is,

  $\begin{array}{c}D=0^2-4\left(0.00012\right)\left(6\right)\\ =-2.88\times {10}^{-3}\end{array}$

Thus, the value of the discriminant is $-2.88\times {10}^{-3}$ .

b.

To determine

To describe: The discriminant of the function $y=0.00012x^2+6$ .

Answer to Problem 62STP

Modelled equation of supporting cables of Golden Gate Bridge is not correct.

Explanation of Solution

Given information:

The supporting cables of the Golden Gate Bridge are shaped like parabola and modelled by equation $y=0.00012x^2+6$ where x is the distance from axis of symmetry and y is the height of cables.

Formula used:

For a quadratic equation $a{x}^2+bx+c=0$ the discriminant Dis $D=b^2-4ac$ .

Calculation:

Consider the equation $0.00012x^2+6=0$

Recall that for a quadratic equation $a{x}^2+bx+c=0$ the discriminant Dis $D=b^2-4ac$ .

Therefore, discriminant of provided equation is,

  $\begin{array}{c}D=0^2-4\left(0.00012\right)\left(6\right)\\ =-2.88\times {10}^{-3}\end{array}$

Since, discriminant is negative so equation will have imaginary zeros. In real time this does not valid. Equation must have real zeros.

Thus, the modelled equation of supporting cables of Golden Gate Bridge is not correct.