Question

A soccer ball was kicked from ground level. It followed a path given by the relation:

h = -0.25d² + 5d,
where h is the height above the ground and d is the horizontal distance, both in meters.
write the relation in intercept form.

Answer 1

The equation in intercept form is h = -0.25(d)(d - 20), which reveals the parabola's x-intercepts to be 0 and 20.

Step-by-step explanation:

The student is dealing with a quadratic equation that describes the height of a soccer ball as a function of the horizontal distance traveled. The given equation is h = -0.25d² + 5d. To write this equation in intercept form, we need to factor out the common factors and write it in the form (d - r1)(d - r2) where r1 and r2 are the x-intercepts of the parabola.

Firstly, we factor out a -0.25 which is common in both terms:

h = -0.25(d² - 20d)

Next, we need to find the roots of the quadratic equation d² - 20d = 0. Factoring d we get:

d(d - 20) = 0

Therefore, the roots (x-intercepts) are d = 0 and d = 20. Now, we write the function in intercept form:

h = -0.25(d)(d - 20)

The given relation, h = -0.25d² + 5d, represents the height of a soccer ball above the ground (h) in meters as a function of the horizontal distance (d) in meters. To write the relation in intercept form, we need to express it as a product of two binomials. First, we can factor out -d from the equation as follows: h = -d(0.25d - 5). Now, we can set each factor equal to zero to find the intercepts. Setting -d = 0 gives us d = 0 as one intercept, and setting 0.25d - 5 = 0 gives us d = 20 as the other intercept.