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Which statement describes the graph of f(x) = x² - 6x + 9?

a line with an x-intercept of (-3, 0)
a parabola with an x-intercept of (-3, 0)
a line with an x-intercept of (3, 0)
a parabola with an x-intercept of (3, 0)

User Peracek
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1 Answer

2 votes

Answer:

A parabola with an x-intercept of (3, 0)

Explanation:

We can immediately rule out the first and third options, because the equation of a second degree function is a parabola.

Your equation is

ƒ(x) = x² - 6x + 9 = 0

We can factor this equation as

ƒ(x) = (x - 3)²

The parent parabola, y = x², has its x-intercept at (0,0).

Your function subtracts three from x, so the intercept is shifted three units to the right.

The graph of your function is a parabola with an x-intercept of (3, 0).

The figure below shows the graph of your function shifted three units by subtracting three from x.

Which statement describes the graph of f(x) = x² - 6x + 9? a line with an x-intercept-example-1
User Azhar Khan
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