Which of the following equations describes the graph?
a.y=-2x^2+2x+3
b.y=-2x^2-2x-3
c.y=2x^2+2x+3
d.y=-2x^2+2x-3

Step-by-step explanation:

Graph of Functions

Given a function f(x), we can sketch the graph of f(x) in many ways. One of the most used is constructing a table of x-y values, giving x any desired value and computing the y-value.

The graph shows the typical shape of a parabola; all the options correspond to parabolas, but only one of them is correct. The parabolas can be concave up or concave down, depending on the sign of the coefficient of the x-squared term. If it's negative, the parabola is concave down, like the one in the graph. So our function cannot be the option C

From the image, we can see two points (0,3) and (1,-3). Testing those points in option A we can see that for x=0, y should be -3 and it's 3.

Testing the point x=1 in the option B results y=-5 and it should be -3. The only possible function is option D, where f(1)=-3 as expected.

Option D.