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Mariana [72]
3 years ago
15

Solve the quadratic by factoring 2X²-2X-12=0

Mathematics
2 answers:
olchik [2.2K]3 years ago
7 0
2x^2-2x-12=0\\\\2x^2+4x-6x-12=0\\\\2x(x+2)-6(x+2)=0\\\\(x+2)(2x-6)=0\iff x+2=0\ \vee\ 2x-6=0\\\\x=-2\ \vee\ x=3
kupik [55]3 years ago
3 0
2x^2-2x-12=0\\
2(x^2-x-6)=0\\
2(x^2-3x+2x-6)=0\\
2(x(x-3)+2(x-3))=0\\
2(x+2)(x-3)=0\\
x=-2 \vee x=3
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y, in terms of time the rain fell, x. ​ ​The time is measured in hours after ​12:00 P.M., with x=0 corresponding to the time 12:
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y, in terms of time the rain fell, x.

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The data set represents a month-to-month progression of gasoline prices over the course of several months in an unspecified city
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The quadratic regression equation for this data set is \rm y=-0.143x^2+0.59x+2.82\\.

<h3>What is the general form of a quadratic equation?</h3>

The general form of the quadratic equation is given by;

\rm ax^2+bx+c=0

Where; a, b, and c are the constants.

x;   0       1         2        3          4         5

y;  2.82  3. 29  3. 46  3. 33   2. 88  2. 24

From the table when the value of x = 0 the value of y is 2.82.

Then,

\rm y=ax^2+bx+c\\\\x=0\\\\2.82=a0^2+b(0)+c\\\\c=2.82

From the table when the value of x = 3 the value of y is 3.33.

\rm y=ax^2+bx+c\\\\x=3\\\\2.82=a(3)^2+b(3)+c\\\\9a+3b+2.82=2.82\\\\9a=-3b\\\\b=-3a\\\\

From the table when the value of x = 5 the value of y is 2.24.

\rm y=ax^2+bx+c\\\\x=3\\\\2.24=a(5)^2+(-3a)(5)+c\\\\25a-15a+2.82=2.24\\\\40a=2.24-2.82\\\\10a=-0.68\\\\a= \dfrac{-0.68}{10}\\\\a=-0.143

And the value of b is;

\rm b=3a\\\\b=3(-0.14)\\\\b=0.59

Therefore,

The quadratic regression equation for this data set is;

\rm y=ax^2+bx+c\\\\y=-0.143x^2+0.59x+2.82\\\\

Hence, the quadratic regression equation for this data set is \rm y=-0.143x^2+0.59x+2.82\\.

To know more about the Quadratic equation click the link given below.

brainly.com/question/14935613

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