Question

A wolf leaps out of the bushes and takes a hunter by surprise. Its trajectory can be mapped by the equation y = −x2 + 12x − 11, write f(x) in intercept form and find how far the wolf leaped using zeros of the function.

Answer 1

To write the function in intercept form, we find the x-intercepts of the function and set the equation equal to 0. The x-intercepts are x = 1 and x = 11. The distance the wolf leaped is 1 unit and 11 units.

Step-by-step explanation:

Finding the Intercept Form

To write the function in intercept form, we need to find the x-intercepts (zeros) of the function. The x-intercepts occur when y = 0, so we set the equation equal to 0 and solve for x:

0 = -x^2 + 12x - 11

Next, we can factor the quadratic to find the x-intercepts:

0 = (x - 1)(x - 11)

Setting each factor equal to 0, we find the x-intercepts:

x - 1 = 0 → x = 1

x - 11 = 0 → x = 11

Therefore, the intercept form of the function is f(x) = -(x - 1)(x - 11)

Calculating the Distance Leap

To find the distance the wolf leaped, we need to find the x-values where y = 0. This occurs at the x-intercepts we found earlier: x = 1 and x = 11. Therefore, the wolf leaped a distance of 1 unit and 11 units.

Answer 2

`y = -x^2 + 12x - 11`

f(x) in intercept form

General equation of intercept form of quadratic equation is

`y=a(x-b)(x-c)`

To get intercept form we factor the right hand side of the given equation

`y = -x^2 + 12x - 11`

Factor out -1

`y = -1(x^2 - 12x + 11)`, factor x^2 - 12x +11

`y = -1(x-11)(x-1)` -------> Intercept form

To find zeros of the function, we replace y with 0

then we set each factor =0 and solve for x

0=-1(x-11)(x-1)

x-11 =0 and x-1=0

x= 11 and x=1

Now we subtract the zeros

11-1 = 10

the wolf leaped about 10 meters (units not mentioned in the question)