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.

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lisboa lisboa · Answer 1 · 2018-09-20T00:51:52+02:00

[tex]y = -x^2 + 12x - 11[/tex]

f(x) in intercept form

General equation of intercept form of quadratic equation is

[tex]y=a(x-b)(x-c)[/tex]

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

[tex]y = -x^2 + 12x - 11[/tex]

Factor out -1

[tex]y = -1(x^2 - 12x + 11)[/tex], factor x^2 - 12x +11

[tex]y = -1(x-11)(x-1)[/tex] -------> 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)