Question

what is the x-intercept of the graph of the function f(x)=x2-16x+64?

Answer 1

Answer:

x-intercept: (8,0)

Step-by-step explanation:

Given: $f(x)=x^2-16x+64$

For x-intercept, Put y=0 and solve for x.

x-intercept: It is a point where y-coordinate zero.

$x^2-16x+64=0$

$x^2-8x-8x+64=0$

$(x-8)(x-8)=0$

Equate each factor to 0 and solve for x

x-8 = 0    , x-8 = 0

x=8,8

x-intercept: (8,0)

Hence, The x-intercept is 8.

Answer 2

The x-intercept of the function is 8

The equation of the function is given as:

$f(x) = x^2 - 16x + 64$

Expand the equation

$f(x) = x^2 - 8x - 8x + 64$

Factorize the above equation

$f(x) = x(x - 8) - 8(x -8)$

Factor out x - 8

$f(x) = (x - 8) (x -8)$

Set f(x) to 0, to calculate the x-intercept

$(x - 8) (x -8)=0$

Rewrite as:

$(x - 8)^2=0$

Take the square roots of both sides

$x - 8=0$

Solve for x

$x = 8$

Hence, the x-intercept of the function is 8

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