Need help with height function problem

[landcleaver202]

A frog leaps from a stump and lands on the ground. His height above the ground can be described by the function h(x)=-x^2/2 + 5x/4 + 3 where "x" is the frog's horizontal distance from the base of the stump, x and h(x) are both in feet and both are positive.
a.) How high is the stump?
b.) How far away from the stump is the frog's landing position?
c.) At what horizontal distance from the base of the stump did the frog reach its highest point.
d.) What was the max height reached by the frog?

 

[Deleted member 4993]

A frog leaps from a stump and lands on the ground. His height above the ground can be described by the function h(x)=-x^2/2 + 5x/4 + 3 where "x" is the frog's horizontal distance from the base of the stump, x and h(x) are both in feet and both are positive.
a.) How high is the stump?
b.) How far away from the stump is the frog's landing position?
c.) At what horizontal distance from the base of the stump did the frog reach its highest point.
d.) What was the max height reached by the frog?

This is an equation of a parabola. What are the coordinates of the vertex of the parabola? Where are the x-intercepts of the parabola? What are your thoughts?

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[stapel]

A frog leaps from a stump and lands on the ground. His height above the ground can be described by the function h(x)=-x^2/2 + 5x/4 + 3 where "x" is the frog's horizontal distance from the base of the stump, x and h(x) are both in feet and both are positive.
a.) How high is the stump?

Before he jumps, he's on the stump. So, at t = 0, he's on the stump. What is his height at t = 0?

b.) How far away from the stump is the frog's landing position?

"Landing" means "on the ground", at which point his height above the ground is h(x) = 0. What is x when h(x) = 0?

c.) At what horizontal distance from the base of the stump did the frog reach its highest point.

This is a quadratic. The max/min point is at the vertex. What did you get for this?

d.) What was the max height reached by the frog?

The x-value of the vertex is the horizontal distance. The h(x)-value of the vertex is the height. What did you get for this?

Please be complete. Thank you!

 

[Ishuda]

A frog leaps from a stump and lands on the ground. His height above the ground can be described by the function h(x)=-x^2/2 + 5x/4 + 3 where "x" is the frog's horizontal distance from the base of the stump, x and h(x) are both in feet and both are positive.
a.) How high is the stump?
b.) How far away from the stump is the frog's landing position?
c.) At what horizontal distance from the base of the stump did the frog reach its highest point.
d.) What was the max height reached by the frog?

Turn each question into its math equivalent assuming a level top of the stump, a 'straight up & down' stump in the area of the base and that the frog jumps 'out' from the top of the stump directly above the base:
a) What is the height function at x=0?
b) What is the value of x when h(x) is zero?
c) Is the maximum of h(x) between x=0 and the value of the x in b) [is the derivative zero in that interval and, if so, is it a maximum) or is the maximum of h(x) at x=0 (since we know the other end point is when the frog reaches the ground below the stump)?
d) What is that maximum h(x) in c).

Please show us your work so we will know where to help.