Mathematics: Look at the quadratic regression equation below to answer the following question: y=-2.096x^2 -2.25x + 9.038 for what value of x is y= -40? (use the quadratic formula to solve the problem.)

1.34 is the answer I think I’m not sure...

Look at the quadratic regression equation below

10040813

11.01.2022

x=4.330,-5.403

Step-by-step explanation:

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$y=-2.096x^{2} -2.25x+9.038$

For y=-40

substitute

$-40=-2.096x^{2} -2.25x+9.038$

$-2.096x^{2} -2.25x+9.038+40=0$

$-2.096x^{2} -2.25x+49.038=0$

$a=-2.096\\b=-2.25\\c=49.038$

substitute in the formula

$x=\frac{-(-2.25)(+/-)\sqrt{-2.25^{2}-4(-2.096)(49.038)}} {2(-2.096)}$

$x=\frac{2.25(+/-)\sqrt{416.197}} {-4.192}$

$x=\frac{2.25(+/-)20.401} {-4.192}$

$x=\frac{2.25(+)20.401} {-4.192}=-5.403$

$x=\frac{2.25(-)20.401} {-4.192}=4.330$

therefore

x=4.330,-5.403

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