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The equation models the height,
h, in feet above the water for a cable in a suspension bridge at a horizontal distance,
x, in feet from the beginning of the span.

h=0.0002(x-1,955)^(2)+100
How many feet above the water is the lowest point on the cable?

The equation models the height, $h$ , in feet above the water for a cable in a suspension bridge at a horizontal distance, $x$ , in feet from the beginning of the span. $\newline$ $h=0.0002(x-1,955)^{2}+100$ $\newline$ How many feet above the water is the lowest point on the cable?

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Write linear functions: word problems

Full solution

Q. The equation models the height,

h

, in feet above the water for a cable in a suspension bridge at a horizontal distance,

x

, in feet from the beginning of the span.

\newline

h=0.0002(x-1,955)^{2}+100

\newline

How many feet above the water is the lowest point on the cable?

Determining the Lowest Point: To find the lowest point on the cable, we need to determine the value of $h$ when the expression inside the parentheses is minimized. Since the expression is squared, the smallest value it can have is $0$ , which occurs when $x$ equals $1,955$ .
Substituting $x$ into the Equation: We substitute $x = 1,955$ into the equation to find the height at the lowest point. $h = 0.0002(1,955 - 1,955)^{2} + 100$
Calculating the Expression Inside the Parentheses: Calculate the expression inside the parentheses: $1,955 - 1,955 = 0$
Squaring the Result: Now, we square the result: $0^{2} = 0$
Multiplying by the Coefficient: Multiply by the coefficient $0.0002$ : $\newline$ $0.0002 \times 0 = 0$
Finding the Height Above the Water: Finally, add $100$ to find the height above the water: $\newline$ $h = 0 + 100$ $\newline$ $h = 100$

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