It seems like we have very little information, but using the axis of symmetry we can plot two more points.
From the graph above, we can see that the parabola must open downward. Next, we will draw a curve that passes through all the points, with a vertex on the line x=2.
Alternative Solution
Finding the Equation
Let's start writing the vertex form of a parabola.
y = a(x-h)^2 + k
In this form, the vertex is (h,k). Since the axis of symmetry is x=2, then h=2.
y = a(x-2)^2 + k
To find the values of a and k we use the fact that the y-intercept is (0,1) and that the graph passes through (3,2.5) to obtain two equations.
y-intercept: (0,1)
Point: (3,2.5)
1 = a(0-2)^2+k
2.5 = a(3-2)^2+k
1 = 4a+k
2.5 = a+k
Next, we will write the left-hand side equation and the right-hand side equation as a system of equations and solve it.
We obtain k = 3. Let's substitute it into the first equation.
a = 2.5 - 3 ⇔ a = - 0.5
We have found the equation of the given parabola.
y = -0.5(x-2)^2 + 3
From the equation above, we know that the parabola opens downward and has its vertex at (2,3). Finally, let's make a graph.
