Equations can be represented on graphs by plotting the corresponding x and y values. The graph of [tex]y = \frac{3}{2}x^2 + 4x - 2[/tex] is option (B).
Given that:
[tex]y = \frac{3}{2}x^2 + 4x - 2[/tex]
First, we check the y intercept of [tex]y = \frac{3}{2}x^2 + 4x - 2[/tex]
This is when [tex]x = 0[/tex]
So, we have:
[tex]y = \frac{3}{2}x^2 + 4x - 2[/tex]
[tex]y = \frac{3}{2} \times 0^2 + 4\times 0 - 2[/tex]
[tex]y = - 2[/tex]
This point is represented as: [tex](0,-2)[/tex]
Next, check the equation when [tex]x = 1[/tex]
So, we have:
[tex]y = \frac{3}{2}x^2 + 4x - 2[/tex]
[tex]y = \frac{3}{2} \times 1^2 + 4\times 1 - 2[/tex]
[tex]y = 3.5[/tex]
This point is represented as: [tex](1,3.5)[/tex]
From the list of given options (see attachment).
Only graph B has the [tex](0,-2)[/tex] and [tex](1,3.5)[/tex] on its curve.
Hence, option (B) is correct.
Read more about equation of graphs at:
https://brainly.com/question/1971145
