Question

Ben is climbing a tree with a lot of branches. His height off the ground at time $t$ is $2t^2-5t+29$ feet. To the nearest foot, what will his minimum height be?

Answer 1

Ben minimum height above the ground when climbing the tree would be 25.875 feet

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

Given that:

h(t) = 2t² - 5t + 29

The minimum height is at h'(t) = 0, hence:

h'(t) = 4t - 5

4t - 5 = 0

t = 5/4

h(5/4) = 2(5/4)² - 5(5/4) + 29 = 25.875 feet

Ben minimum height above the ground when climbing the tree would be 25.875 feet

Find out more on equation at: brainly.com/question/2972832

Answer 2

Using the vertex of the quadratic equation, it is found that his minimum height will be of 25.875 feet.

What is the vertex of a quadratic equation?

A quadratic equation is modeled by:

$y = ax^2 + bx + c$

The vertex is given by:

$(x_v, y_v)$

In which:

$x_v = -\frac{b}{2a}$

$y_v = -\frac{b^2 - 4ac}{4a}$

Considering the coefficient a, we have that:

• If a < 0, the vertex is a maximum point.

• If a > 0, the vertex is a minimum point.

In this problem, the equation is:

h(t) = 2t² - 5t + 29.

Hence the coefficients are a = 2 > 0, b = -5, c = 29, and the minimum height in feet is given by:

$y_v = -\frac{(-5)^2 - 4(2)(29)}{4(2)} = 25.875$

More can be learned about the vertex of a quadratic equation at brainly.com/question/24737967