Question

a quadratic equation is shown below: x2 18x 76 = 0 which of the following is the first correct step to write the above equation in the form (x − p)2 = q, where p and q are integers? add 9 to both sides of the equation add 5 to both sides of the equation subtract 5 from both sides of the equation subtract 9 from both sides of the equation --------------------------------------- which statement best describes the graph of x3 − 3x2 − x 3? it starts down on the left and goes up on the right and intersects the x-axis at x = −1, 2, and 3. it starts down on the left and goes up on the right and intersects the x-axis at x = −1, 1, and 3. it starts up on the left and goes down on the right and intersects the x-axis at x = −1, 2, and 3. it starts up on the left and goes down on the right and intersects the x-axis at x = −1, 1, and 3. ------------------------------------------ a batter hits a baseball upward with an initial speed of 96 feet per second. after how many seconds does the ball hit the ground? use the formula h = rt − 16t2 where h represents height in feet and r represents the initial speed. ------------------------------------------- a ball is thrown upward from the top of a building. the function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds: f(t) = −16t2 34t 80 the average rate of change of f(t) from t = 5 seconds to t = 7 seconds is _____ feet per second.

Answer 1

1.) add 5 to both sides of the equation.

2.) it starts down on the left and goes up on the right and intersects the x-axis at x = −1, 1, and 3

3.) 0 = 96t - 16t^2 = 16t(6 - t)
t = 0 or t = 6

4.) f(t) = -16t^2 + 34t - 80
Average rate of change = (f(7) - f(5))/(7 - 5)
f(7) = -16(7)^2 + 34(7) - 80 = -16(49) + 238 - 80 = -784  + 158 = -626
f(5) = -16(5)^2 + 34(5) - 80 = -16(25) + 170 - 80 = -400 + 90 = -310

Average rate of change = (-626 - (-310))/2 = -316/2 = -158 feet per second.

Answer 2

The average rate of change will be equal to -158 feet per second.

What is a quadratic equation?

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

The solution to the question is given as:-

1.) Add 5 to both sides of the equation.

2.) it starts down on the left and goes up on the right and intersects the x-axis at x = −1, 1, and 3

3.) 0 = 96t - 16t^2 = 16t(6 - t)

t = 0 or t = 6

4.) f(t) = -16t^2 + 34t - 80

The average rate of change

= (f(7) - f(5))/(7 - 5)

f(7) = -16(7)^2 + 34(7) - 80 = -16(49) + 238 - 80 = -784  + 158 = -626

f(5) = -16(5)^2 + 34(5) - 80 = -16(25) + 170 - 80 = -400 + 90 = -310

Therefore the Average rate of change

= (-626 - (-310))/2 = -316/2 = -158 feet per second.

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