Question

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 help solve the problem.)

Answer 1

D

Explanation:

!

Answer 2

`x=4.330,-5.403`

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`

so

`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(+/-)√(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`