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K) I, II, and III

Step-by-step explanation:

Given the quadratic equation in standard form, h = -at² + bt + c, where h is the height or the projectile of a baseball that changes over time, t.  In the given quadratic equation, c represents the constant term. Altering the constant term, c, affects the h-intercept, the maximum value of h, and the t-intercept of the quadratic equation.  

The h-intercept is the value of the height, h, when t = 0. This means that setting t = 0 will leave you with the value of the constant term. In other words:

Set t = 0:

h = -at² + bt + c

h = -a(0)² + b(0) + c

h = -a(0) + 0 + c

h = 0 + c

h = c

Therefore, the value of the h-intercept is the value of c.

Hence, altering the value of c will also change the value of the h-intercept.

The maximum value of h occurs at the vertex, (t, h ). Changing the value of c affects the equation, especially the maximum value of h. To find the value of the t-coordinate of the vertex, use the following formula:

t = -b/2a

The value of the t-coordinate will then be substituted into the equation to find its corresponding h-coordinate. Thus, changing the value of c affects  the corresponding h-coordinate of the vertex because you'll have to add the constant term into the rest of the terms within the equation. Therefore, altering the value of c affects the maximum value of h.

The t-intercept is the point on the graph where it crosses the t-axis, and is also the value of t when h = 0. The t-intercept is the zero or the solution to the given equation. To find the t-intercept, set h = 0, and solve for the value of t.  Solving for the value of t includes the addition of the constant term, c, with the rest of the terms in the equation.  Therefore, altering the value of c also affects the t-intercept.

Therefore, the correct answer is Option K: I, II, and III.

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.