How do you find the axis of symmetry, graph and find the maximum or minimum value of the function $y = 2 x^{2} - 6 x - 36$ $y = 2x^2 - 6x - 36$ ?

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How do you find the axis of symmetry, graph and find the maximum or minimum value of the function $y = 2 x^{2} - 6 x - 36$ $y = 2x^2 - 6x - 36$ ?

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Answer 1 · 2017-07-25T05:59:51

The function has a minimum at $x = 1.5$ $x=1.5$

Axis of symmetry $x = 1.5$ $x=1.5$

Explanation:

Given -

$y = 2 x^{2} - 6 x - 36$ $y=2x^2-6x-36$
$\frac{d y}{d x} = 4 x - 6$ $dy/dx=4x-6$
$\frac{d^{2} y}{{d x}^{2}} = 4 > 0$ $(d^2y)/(dx^2)=4>0$
$\frac{d y}{d x} = 0 \Rightarrow 4 x - 6 = 0$ $dy/dx=0 =>4x-6=0$
$x = \frac{6}{4} = 1.5$ $x=6/4=1.5$

At $x = 1.5; \frac{d y}{d x} = 0; \frac{d^{2} y}{{d x}^{2}} > 0$ $x=1.5; dy/dx=0;(d^2y)/(dx^2)>0$

The function has a minimum at $x = 1.5$ $x=1.5$

Axis of symmetry $x = 1.5$ $x=1.5$

Graph -

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How do you find the axis of symmetry, graph and find the maximum or minimum value of the function $y = 2 x^{2} - 6 x - 36$ $y = 2x^2 - 6x - 36$ ?

1 Answer

Explanation:

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How do you find the axis of symmetry, graph and find the maximum or minimum value of the function y=2x2−6x−36y = 2x^2 - 6x - 36?

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Explanation:

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How do you find the axis of symmetry, graph and find the maximum or minimum value of the function $y = 2 x^{2} - 6 x - 36$ $y = 2x^2 - 6x - 36$ ?