What are the x-intercepts of the graph of the function f(x) = x² + 4x - 12?

Solution:

It is given that

f(x) = x² + 4x - 12

The x-intercept can be found by considering y as 0

x² + 4x - 12 = 0

Splitting the middle term

x² - 2x + 6x - 12 = 0

Taking out the common terms

x (x - 2) + 6 (x - 2) = 0

(x - 2) (x + 6) = 0

So the x intercepts are 2 and -6.

The y-intercept can be found by considering x as 0

f(0) = 0² + 4 (0) - 12

So we get

f(0) = -12

Therefore, the x-intercepts of the graph are (2, 0) and (-6, 0).

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What are the x-intercepts of the graph of the function f(x) = x² + 4x - 12?

Summary:

The x-intercepts of the graph of the function f(x) = x²+4x-12 are (2, 0) and (-6, 0).