Homework Clinic
Mathematics Clinic => Grade 10 Mathematics => Topic started by: Jones on Jun 18, 2013
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I've been trying really hard to figure out these for Precalc, but I just don't understand. How do I solve this quadratic using vertex form?
4x^2 + 149 = 28x
and this one, using root form?
3x + 8 + 16/3x = 0
thanks so much!
never mind the root form bit. apparently, that's just basic factoring.
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You find the vertex of a quadratic function by completing the square.
4x^2 - 28x + 149 = y
4(x^2 - 7x) = y - 149
x^2 - 7x = (1 / 4)(y - 149)
x^2 - 7x + (7 / 2)^2 = (1 / 4)(y - 149 + 49)
= (1 / 4)(y - 100)
(x - 7 / 2)^2 = (1 / 4)(y - 100)
That's the vertex form of the equation, giving vertex (7 / 2, 100).
With y = 0, it gives:
x - 7 / 2 = +/- 5i
x = 7 / 2 +/- 5i.