Question

f(x)= -4(x-2)^2+100 answer all questions below show work if there is any.
a) find the y-intercept(s) (write your answer(s) as ordered pairs)
b) Find the vertex
c) Find the x-intercept(s) (write your answer(s) as ordered pairs)
e) what is the domain of the function? (use interval notation)
f) what is the range of the function? ( use interval notation)

Answer 1

The vertex of the given function $f(x)= -4(x-2)^2+100$ is (2, -25). the y-intercept is (0,-21). the x-intercept are (-3,0) and (7,0).

What is x-intercept of a function?

The x-intercept of a function of variable x ( y = f(x) ) form is an intersection fo the x-axis and the curve of the function.

The x-intercept for a function y = f(x) is a solution to the equation f(x) = 0 because at that value of x, the function f(x) lies on x-axis,

where y is 0. Values of x-intercept for a function f(x) are also called roots or solution of f(x) = 0 equation.

We have the function,

$f(x)= -4(x-2)^2+100$

On simplifying, we get,

$f(x)= x^2 - 4x -21\\\\f(x) = (x+3)(x-7)$

Now, the factors of the given functions are (x+3) and (x - 7).

We have,an intercept form of the function is .

$f(x) = (x+3)(x-7)$

Now, we know that,

Value of x-coordinate of the vertex is -b/2a

= 4 / 2

= 2

x = 2

Then,

$f(2)= 2^2 - 4(2) -21\\\\f(2)= -25$

So, the vertex of the function is (2, -25).

Further, we know that 'the y-intercept of a function is the point where the function crosses the y-axis'.

So, when x=0, we have,  i.e. f(0) = -21

Thus, the y-intercept is (0,-21)

Also, 'the x-intercept of a function is the point where the function crosses x-axis'.

Then, for f(x)=0, we have  i.e.  i.e. x= -3 and x= 7

Thus, the x-intercept are (-3,0) and (7,0).

Learn more about x-intercept here:

https://brainly.com/question/14764115

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