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mihalych1998 [28]
3 years ago
15

A ball was tossed up into the air. The height of the ball as a function of the time the ball is in the air in seconds can be mod

eled by a quadratic function. At the time the ball was initially thrown in the air, it was 7. 5 meters off the ground. After 1. 25 seconds, the ball was at its maximum height of 15. 3125 meters. What was the height of the ball 2 seconds after being thrown? Round your answer to the nearest tenth as needed. Meters.
Mathematics
1 answer:
Andrei [34K]3 years ago
3 0

The height of the ball 2 seconds after being thrown is 20.8m

In order to get the required quadratic function, we need to write the given information as coordinate.

  • If the time the ball was initially thrown in the air, it was 7. 5 meters off the ground, this is written in a coordinate form as (0, 7.5)

  • If after 1. 25 seconds, the ball was at its maximum height of 15.3125 meters in a coordinate form as (1.25, 15.3125)

Get the slope of the equation;

m=\frac{15.3125-7.5}{1.25-0}\\m= \frac{7.8125}{1.25}\\m= 6.25

Get the y-intercept "b"

Recall that y = mx + b

7.5=6.25(0) + b\\7.5 = b\\ b= 7.5

Get the required equation:

y = 6.65x + 7.5

Next is to get the height of the ball 2 seconds after being thrown

y = 6.65x + 7.5\\y = 6.65(2)+ 7.5\\y=13.3 + 7.5\\y=20.8m

Hence the height of the ball 2 seconds after being thrown is 20.8m

Learn more on functions here: brainly.com/question/1214333

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Answer: I'm not going to give out the answers but I'm happy to explain it and help you out if you're still confused. I'm a geometry honors student rn btw just so you know my credentials.

Step-by-step explanation:

To find slope and write it in slope-intercept form you first need to know the equation and what different variables represent.

y = mx + b is the equation for slope-intercept. You need to find what m and b are to right a slope-intercept equation. for example the first problem's answer is y = \frac{-1}{2}x + 1

m is slope which is the angle that the line is at. To find slope or m, you need to choose a point on the graph. Then, count the amount of spaces vertically and horizontally until the next point on the graph. When I say point, I'm referring to a place on the graph where the line cross perfectly over the intersection of two lines on the graph. Slope is always 'rise over run' meaning it is a fraction containing the amount up or down, over the amount left or right. For example, the first problem (the one on the top left) the slope is  \frac{-1}{2} .

b is the y-intercept. The y intercept where the line crosses the y-axis which is that bold line going up and down in the middle. For example in number one, the y-intercept is 1 because it is one unit up from the origin. (the origin is 0,0, or the very middle of the graph).

Hope this helps! :)

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