Question

I need a lot of help from the smartest people now right now

Answer 1

Answer:

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.  

I. The h-intercept

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.

II. The maximum value of h

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.

III. The t-intercept

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.