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Home Q & A Board Science-Related Homework Help Mathematics
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smmrwds smmrwds
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11 years ago
I understand that one needs to use the quadratic formula to find the x-intercepts, but then I don't know how to find the vertex to sketch the parabola of the inequality. Could you help me out?

Thanks in advance!
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#1
11 years ago
Given: f(x) = ax² + bx + c

The vertex = (-b/2a, f(-b/2a))

You can also write f(x) = ax² + bx + c in the form of f(x) = a(x - h)² + k, where (h,k) is the vertex, but that involves completing the square.

Example 1:  Find the vertex of f(x) = 2x² - 4x + 5

-b/2a ===> 4 / (2*2)  = 1

f(1) = 3

So, the vertex is (1,3).

Example 2: Find the vertex by writing f(x) in the form of a(x - h)² + k

f(x) = 2x² - 4x + 5

2(x² - 2x + ?) + 5 - 2?

? = (-2/2)² = 1

2(x² - 2x + 1) + 5 - 2

2(x - 1)² + 3  <==== h = 1, k = 3

vertex = (1,3)
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