Final answer:
To graph the parabola with vertex (0,2) and point (3, -5), substitute the values into the equation y = ax^2 + 2. Solve for the value of a and plot the graph.
Step-by-step explanation:
To graph the parabola with vertex (0,2) and point (3, -5), we can use the standard form of the equation of a parabola, which is y = a(x - h)^2 + k, where (h, k) represents the vertex.
Substituting the values (0,2) into the equation, we get the equation y = a(x - 0)^2 + 2. Simplifying, we have y = ax^2 + 2.
Now, we can substitute the given point (3, -5) into the equation to solve for the value of a. Plugging in these values, we have -5 = a(3)^2 + 2. Simplifying and solving for a, we get a = -1.
Substituting the value of a back into the equation y = ax^2 + 2, we have y = -x^2 + 2.
Plotting the graph using the equation y = -x^2 + 2 will give us the parabola with vertex (0,2) and point (3, -5).