What is the vertex form of $y = (3 x - 8) (- 6 x - 2) + 2 x^{2} + 3 x$ $y= (3x-8)(-6x-2)+2x^2+3x$ ?

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What is the vertex form of $y = (3 x - 8) (- 6 x - 2) + 2 x^{2} + 3 x$ $y= (3x-8)(-6x-2)+2x^2+3x$ ?

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Answer 1 · 2018-06-02T06:47:20

Vertex $(\frac{45}{32}, \frac{3049}{64})$ $(45/32, 3049/64)$

Explanation:

$y = (3 x - 8) (- 6 x - 2) + 2 x^{2} + 3 x$ $y=(3x-8)(-6x-2)+2x^2+3x$

$y = - 18 x^{2} - 6 x + 48 x + 16 + 2 x^{2} + 3 x$ $y=-18x^2-6x+48x+16+2x^2+3x$

$y = - 16 x^{2} + 45 x + 16$ $y=-16x^2+45x+16$

The vertex is found by $x = - \frac{b}{2 a}$ $x=-b/(2a)$

By looking at the general formula of a quadratic function,
$y = a x^{2} + b x + c$ $y=ax^2+bx+c$ , we can see that $b = 45$ $b=45$ and $a = - 16$ $a=-16$

$x = - \frac{b}{2 a} = - \frac{45}{2 \times - 16} = \frac{45}{32}$ $x=-b/(2a) = -45/(2times-16) = 45/32$

Sub $x = \frac{45}{32}$ $x=45/32$ into $y = - 16 x^{2} + 45 x + 16$ $y=-16x^2+45x+16$

$y = - 16 {(\frac{45}{32})}^{2} + 45 (\frac{45}{32}) + 16$ $y=-16(45/32)^2+45(45/32)+16$
$y = \frac{3049}{64}$ $y= 3049/64$

Vertex $(\frac{45}{32}, \frac{3049}{64})$ $(45/32, 3049/64)$

You can from the graph below that the vertex is quite high up.

graph{(3x-8)(-6x-2)+2x^2+3x [-10, 10, -5, 5]}

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What is the vertex form of $y = (3 x - 8) (- 6 x - 2) + 2 x^{2} + 3 x$ $y= (3x-8)(-6x-2)+2x^2+3x$ ?

1 Answer

Explanation:

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What is the vertex form of y=(3x−8)(−6x−2)+2x2+3x y= (3x-8)(-6x-2)+2x^2+3x?

1 Answer

Explanation:

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What is the vertex form of $y = (3 x - 8) (- 6 x - 2) + 2 x^{2} + 3 x$ $y= (3x-8)(-6x-2)+2x^2+3x$ ?