Question

Y=3x² + 7x+2-25OA. Graph AB. Graph BOC. Graph CD. Graph D-2525A-5 +

Answer 1

Answer: D. Graph D assuming that it is the last one shown.

Step-by-step explanation

Given

`y=3x²+7x+2`

we can determine the solutions of the equation (the points at which y = 0) and compare them with the graphs given to see which one is the correct one.

To solve the equation, we have to set it to 0:

`0=3x²+7x+2`

Now, we can use the General Quadratic Formula to solve it:

`x_(1,2)=(-b\pm√(b^2-4ac))/(2a)`

where a, b and c represent the coefficients of the equation in the form:

`ax^2+bx+c=0`

Thus, in our case a = 3, b = 7, and c = 2. Replacing the values in the General Quadratic Formula and solving:

`x_(1,2)=(-7\pm√(7^2-4(3)(2)))/(2(3))`
`x_(1,2)=(-7\pm√(49-24))/(6)`
`x_(1,2)=(-7\pm√(25))/(6)`
`x_(1,2)=(-7\pm5)/(6)`

Finally, calculating our two solutions:

`x_1=(-7+5)/(6)=(-2)/(6)=-(1)/(3)`
`x_1=(-7-5)/(6)=(-12)/(6)=-2`

Based on these values, we can see that the graph that has two solutions in the negative numbers is: