William is competing in the shot put event at a track meet. the quadratic expression that models the vertical height of the shot put from the ground, in feet, over the horizontal distance traveled, in feet, x, is given below. -2x^2 + 3x + 5 a. the initial height from which the shot was thrown b. the maximum height of the shot c. the time it takes for the shot to reach the ground d. the horizontal distance covered by the shot.

A. 5 units

B. 6.125 units

C. Can't be determined

D. 2.5 units

Step-by-step explanation:

A. initial height is determined by the y-intercept which is 5

B. Maximum height is given by x-coordinate of vertex of the parabola i.e. 6.125

C. As the graph doesn't give any relation between time and height so the time can't be determined

D. horizontal distance is measured by the distanced traveled along x-axis.

step-by-step explanation:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true