Question

What is the equation of the graph below?

A graph shows a parabola that opens up and does not cross the x axis. The axis of symmetry is x equal negative 2. The parabola crosses through the points negative 1, 4 and negative 3, 4.
y = − (x − 2)2 + 3
y = (x + 2)2 + 3
y = − (x + 3)2 + 2
y = (x − 3)2 + 2

Answer 1

Since the graph opens upward it cannot be the first or third choice.
Option # 2
y = (x + 2)^2 + 3
(-1, 4)
(-3, 4)
y = (-1 + 2)^2 + 3
y = (1)^2 + 3
y = 1 + 3
y = 4 checks
y = (-3 + 2)^2 + 3
y = (-1)^2 + 3
y = 1 + 3
y = 4 checks
Options # 2 is the answer

Answer 2

y = (x+2)^2 + 3, the second one.

This one never crosses the x axis (The last one neither). This one has the vertex in x=-2 (the last one in x=3). Moreover, x=-1, gives (-1+2)^2+3 = 4, and same for x=-3.