Write the vertex of the following function as $\left( x,y \right)$ :

$f\left( x \right) ={ 4x }^{ 2 } -12x + 9$

Find $x+y$

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Check out the set:
2016 Problems
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The answer is 1.5.

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There are $3$ methods to find the vertex of quadratic functions $f(x) = ax^2 + bx + c$

For this question, I will demonstrate

Method 2$f(x) = 4x^2-12x+9\\ =(2x)^2 - 2(3)(2x) + 3^2\\ =(2x-3)^2$

The minimum value of $f(x)$ is $0$ when $2x-3=0 \implies x=\dfrac{3}{2}$

The vertex of $f(x)= \left(\dfrac{3}{2},0\right)$

$x=\dfrac{3}{2},\;y=0,\;x+y=\dfrac{3}{2}+0=\boxed{1.5}$