i need to find the vertex of this equation: 6x^2-15x-9 using to methods, i know method of vertex form but i don't know the other one so if anyone knows please help!!!!!!!!!!!!!
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First of all, that's not an equation. It's an expression.
But since I have such a sweet disposition,
I'll just assume you meant:
6x² - 15x - 9 = 0
Anyways,
it just so happens that I don't like the quadratic formula.
You can use it if you like, but here's a method known as "completing the square:"
6x² - 15x = 9 ← see why an "=" sign is needed?
x² - 5/2x = 3/2
x² - 5/2x + (-5/4)² = 3/2 + 25/16
(x - 5/4)² = 49/16
x - 5/4 = ±7/4
x = 5/4 ± 7/4
x = 3 or x = -1/2 ✔
This is actually the method used to derive
the quadratic formula from 0 = ax² + bx + c
so it's really good to learn.
♣♦
But since I have such a sweet disposition,
I'll just assume you meant:
6x² - 15x - 9 = 0
Anyways,
it just so happens that I don't like the quadratic formula.
You can use it if you like, but here's a method known as "completing the square:"
6x² - 15x = 9 ← see why an "=" sign is needed?
x² - 5/2x = 3/2
x² - 5/2x + (-5/4)² = 3/2 + 25/16
(x - 5/4)² = 49/16
x - 5/4 = ±7/4
x = 5/4 ± 7/4
x = 3 or x = -1/2 ✔
This is actually the method used to derive
the quadratic formula from 0 = ax² + bx + c
so it's really good to learn.
♣♦